Archaic Age God Powers

Rain - Ra
Boosts your own farm gather rates by 300% for one minute, boosts those of other players on the map by 200%. No god powers can be invoked while Rain is in effect. Only affects farms within range of a settlement.
Using Rain:
Because Rain affects enemies, you have incentive to set up farming earlier than normal when playing as Ra - but don't think Rain makes farms a good investment early on - free food is often better until your economy can take the strain of setting up expensive farms. (Unless you are attempting Ra's unique fast heroic, though that is not very popular after the 1.03 patch.) Hence the best time to get ready to use Rain is in mid Classical Age. (This pays even greater divedends for Ra, since the food helps him advance to the Heroic age and take advantage of his Chariot and Camel upgrades.) Before using Rain, make sure you have not only Plow (the first farming upgrade) but also Husbandry. Your villagers will gather super fast once rain is invoked, but without Husbandry to double their carry capacity, they lose lots of potential gathering time walking to the Town Center to drop off their food! Also be sure to have your Pharaoh empowering the Town Center to get the maximum resources from Rain.

Also because Rain affects both allies and enemies, you want to co-ordinate with allies when to use it. (While still trying to set up farming earlier than your enemies.) One particularly effective way of denying your enemy of the additional farming speed from Rain is to advance to the Heroic Age under Hathor, and use the Locust Swarm god power to take out enemy farms prior to using Rain. Alternately, time a raid to hit an enemy town at the time you cast Rain. His villagers will be hiding in the Town Center instead of farming.

Prosperity - Isis
Increases gold mining speed by 80% for 50 seconds.
Using Prosperity:
The best time to use Prosperity is probably during the advance to the Classical Age. Once you've researched Pickaxe, shift some additional villagers temporarily over to gold, make sure the Pharaoh is empowering the mine, and fire off Prosperity. After 50 seconds pass, you should have just hit the Classical age, and you'll have a huge gold stockpile for this early in the game. Take the extra villagers off gold mining to begin erecting your first few Barracks.

Vision - Set
Reveals a large area of the fog of war to the player for 20 seconds.
Using Vision:
A lot of people will be inclined to simply use Vision as soon as the game begins. In my opinion though, you will gain more from this GP by saving it for slightly later in the game. In nearly all games it's pretty easy to figure out where the enemy town is - so it's hardly essential to cast it for this purpose. (Set even gets a bonus scouting unit - the Hyena of Set.)

Instead, if you wait until early in the Classical Age (perhaps 5-7 minutes in a competitive game) and cast it over an enemy town, you will be given full information about where he is gathering resources, (and thus, where you should be attacking) and what units he intends to build. Seeing those telltale first units coming out of his buildings will tell you what you need to counter them. If you had cast it right at the start of the game though, you would have no information about where his villagers are located, or what units he planned to use - merely the location of his town and the geography around it.
Classical Age God Powers
Shifting Sands - Ptah (Ra, Set)
Instantly transports a group of units from one point on the map to another. Can be used to move both the player's units and the enemy's, however it will choose the enemy units to be transported randomly, and may not transport all of them, whereas it will transport most or all of the player's units. Has a reduced effect on enemy villagers.
Using Shifting Sands:
Shiftings Sands is a god power that has two principle uses. The first is to use it to simply take a chunk out of an enemy force. Cast Shifting Sands just before a battle begins to take several units out of an enemy force, and deposit them near your Town Center (early in the game) or Migdol Stronghold (later in the game) where they will get cut to pieces by arrows. This will increase your odds of winning the battle, and cause you to take less damage from it.

The second use of Shifting Sands is to emulate Underworld Passage. If an enemy is relying on walls/cliffs/bodies of water to keep you out, you can give him a nasty surprise by arriving almost instantly via Shifting Sands. However, the GP doesn't seem to always tranport the intended units, even if there are no enemies in the area of effect. It's kind of an unpredictable GP at the very least.

Shifting Sands can take a bit of practice and experimenting to get used to, simply because it requires two mouse clicks that require you to be looking at two different parts of the map to work. Without practice, you can't cast it in a hurry, so don't try to, or you'll only end up catching a single unit rather than several!

Eclipse - Bast (Isis, Ra)
Increases the attack of all myth units (including their special attacks) by 50% and their speed by 20%. Eclipse lasts for just over one minute, and no other god powers can be cast while it is in effect.
Using Eclipse:
This is without doubt the least useful GP in AoM. While it is at least potentially very powerful, in too few games does it have any real bearing on the game's outcome. Deciding when to use it is pretty simple. If you have myth units, and encounter a key battle, cast Eclipse.

You can also use Eclipse to block other GP's. If you note an enemy player has chosen Hermes, for instance, he will be saving the Ceasefire GP for whenever he runs into trouble. Cast Eclipse before you are about to deal a big blow to him to stop him doing this. (Likewise with other 'lifesaver' GP's - Ancestors, Bronze, Flaming Weapons, etc.)

Plague of Serpents - Anubis (Isis, Set)
Summons friendly cobras to guard the target location on the map. The player has no control over the serpents, but shares their line of sight. If cast on water, this god power creates 'sea serpents', which are naval versions of the cobras summoned on land.
Using Plague of Serpents:
Plague of Serpents is a very useful defensive GP. The Serpents themselves are not particularly powerful, but will easily dissuade an enemy from attacking you early on. This can be particularly useful if an enemy is about to attack your economy in the first few minutes of the game and your forces are not substantial enough to repel them. Plague of Serpents is not so useful offensively. Because the Serpents refuse to stray very far from their original location, they will only be useful for one battle. However, if you really need to a win a battle, go ahead and cast it, but be aware of the possibility that the enemy may simply retreat.

Two things to be aware of when casting Plague of Serpents are the facts that a) Serpents do only 10% damage to villagers, and b) they are counted as Myth units. Hence, casting near villagers or heroes is often a bad idea. (A smart player will in fact use either villagers, heroes or ranged units to clear out a patch of snakes that threatens them, since it allows them to do so and take very little damage.) Plague of Serpents can be useful if it is essential to disrupt enemy villagers putting up a structure - perhaps a key tower or fortress would win them the battle, or perhaps you want to slow down their advance by stopping a temple going up - but is no good for simply trying to disrupt a resource gathering operation. The villagers can just stop their task, kill the snakes, and go back to work.

Plague of Serpents, while it can be cast on water, isn't very useful when used thus. The serpents will not attack anything outside a certain range, so well managed arrow ships can simply retreat to avoid being attacked by them, and then with careful management, kill all of them without being retaliated against. It's better saved for casting on land.
Heroic Age God Powers

Locust Swarm - Hathor (Ra, Isis)
Creates three locust swarms that wander randomly around the target area for 20 seconds. Any farms the swarms touch are instantly destroyed. Other units have damage dealt to them. Can only be targeted at a location where there are enemy farms, villagers or fishing boats.
Using Locust Swarm:
Locust Swarm does not provide any direct benefits to the player, however, losing the cost of expensive farms and the management necessary to set them up will be a major blow to any player. In terms of simple cost, you are at the least denying your enemy several hundred wood. Using Locust Swarm is fairly simple. Send a unit to the enemy Town Center to gain LOS of their farms. Fire the GP off. In order to get the greatest potential gain from this god power, cast it in the middle of the battle and your enemy may not notice - or not notice until it's too late and their economy has taken critical damage, because they were spending food without gaining any.

Locust Swarm has two alternate though usually less effective uses. The first is to disrupt a group of enemy Greek or Egyptian builders. If it is essential that you stop a fortress or town center going up and you can't stop it in time, cast Locust Swarm on the villies. They will be unable to build, and will probably die too. (Unfortunately this doesn't work with the Norse, since they construct with military units.) The other use is to try and kill a large concentration of gold miners. You will frequently encounter many enemy villagers on one gold pile, and they will be working close together. Fire Locust Swarm off on them, and you have a good chance of killing the whole lot if they can't get out of the swarms fast enough. (Which will often happen if they are working in cramped situations.)

Ancestors - Nephthys (Isis, Set)
Summons an army of 13 minions over the same number of seconds to serve the player for the god power's duration - one minute in length. When the god power ends, the minions die. Minions are fairly tough melee units with a fast move rate. Ancestors can be cast on water to summon 'lost ships', which like minions will die after one minute's time.
Using Ancestors:
Ancestors is potentially a very powerful GP, but also one you should be careful not to misuse. It gives you an instant army, but one that dies after 60 seconds. Obviously, because the minions lifespan is limited by the time of the GP, do not cast it until a battle has begun - and to stop an enemy from simply running away to let the minions die, try and get his army right into the battle before casting, not just close to your units.

If an enemy runs away from your Ancestors in a bid to wait them out until dying, use your minions (and army) to attack key buildings or his villagers while the god power is in effect - don't waste time chasing after him, your army will only stick around for one minute!

Ancestors are counted as myth units, so enemy heroes will do bonus damage to them - but do not worry overly about this, because of their limited lifespan they'll die anyway. It doesn't matter if they take damage from enemy units - in fact, that's the whole idea.

Citadel - Sekhmet (Ra, Set)
Converts a friendly Town Center into a Citadel, which has 50% more HP, slightly more attack, and supports 25 population.
Using Citadel:
Some people believe the value of a Citadel is in being a powerful offensive tool. Take a forward settlement, build a Town Center, and gain a pseudo-fortress in the form of the Citadel. In truth, while the Citadel is indeed significantly tougher than a Migdol Stronghold, its greatest value is not as a fortress, but in supporting additional population - 10 bonus pop slots can make all the difference. Don't place it in a contested area of the map if you may lose it - since you can't replace those 10 bonus slots. You're better off casting it at home if this is the case.

Also keep in mind that it can be cast on an allied TC. While again, I stress the point that you must do your best to retain the extra population slots granted by Citadel in favor of getting a better offense/defense, it can sometimes help an ailing ally long enough for you to get there and come to his rescue.
Mythic Age God Powers

Son of Osiris - Osiris (Ra, Isis)
Converts the Pharaoh into Son of Osiris, which has greatly increased attack and HP, and hits up to four enemies at once when attacking.a powerful unit with a devastating attack. When Son of Osiris dies, the regular Pharaoh regenerates, so you can only use Son of Osiris once, and he cannot be healed in any way.
Using Son of Osiris:
Son of Osiris is one of the potentially more powerful GP's in the game. The bearing he has on the game isn't random, and isn't time restricted. You have full control over what he can do. Try and keep your Son of Osiris out of harm's way. Surround him with units (preferably the ranged Chariots and Slingers, since they will stay in place around him) to make it harder for enemy melee units to get to, and retreat him out of range of enemy ranged units - since he will inevitably draw the fire of every ranged unit your enemy has.

In between battles remember that Son of Osiris has the same empowering ability as the normal Pharaoh, so use him to speed production of military units and construction of new Migdols or Town Centers in forward areas. Finally, keep in mind your Son of Osiris moves rather slow. If you find you're losing a battle, you'll want to keep him alive, so withdraw him as soon as it's safe, not at the last minute when most of your units are gone.

Tornado - Horus (Ra, Set)
Creates a tornado that deals a large amount of damage to both units and buildings. The tornado will wander randomly about the target area for 20 seconds before dissapearing.
Using Tornado:
Tornado is incredibly powerful, but unfortunately, also very random. The best place to cast it is somewhere where, no matter which direction it chooses to go in, it will damage something important. The ideal spot is an enemy forward base, where there are clusters of important buildings and units being made. Always follow up use of Tornado with an attack so you can take out buildings that were only just damaged and not destroyed, and so you can deny the enemy the opportunity to heal his units in order to recover from the attack.

Keep in mind that Tornado does of course pose the same threat to you as your enemy. It may look like it will stay in the area you want it to, but its random nature makes this even more important to remember. Do not think that you can try and cast it defensively, you'll usually do just as much (if not more) harm than good.

Meteor - Thoth (Isis, Set)
Causes Meteors to rain down randomly over the target area. Meteor strikes do massive amounts of damage to buildings, but not much to units. Lasts 20 seconds.
Using Meteor:
Meteor is definitely the showiest GP in AoM, which makes it very popular with newbies. Its actual effectiveness is somewhat random, and it is never a good idea to use it on units. (Meteors do mostly crush damage.) Meteor is best used on buildings. Target it on an enemy town, and you'll cause some significant damage to his farming, as well as damage many important buildings and defenses. Target it on a forward base to take out a number of buildings and soften up the rest. The meteors probably won't kill any of the units they hit, but any damaged will make your job easier. As with Tornado, always follow up use of Meteor with an attack so your enemy does not have the opportunity to repair the damage dealt by it.