XCOM is based around the premise that squads of soldiers will attempt to capture useful items and info from captured or crashed UFOs. So how do you start?
   First talk to your players and describe the fact that they can play as any type of military or government personnel. They don't have to be SOLDIERS, they can be police officers, security agent "spooks" like the CIA, hitmen, hunters, or even a scientist! Any profession in real life is to open PCs, though some are obviously better than others,  they may even start out as 0-level people and learn military skills as XCOM inducts them into its ranks. Note though, that skilled personnel are NOT 0-level folk, SAS anti-terrorist squads, Marine Force Recon units etc are highly trained folk, ergo they start out at higher level (see Humans for details)
  Because the setting is so lethal, especially at the beginning, players should make at least one backup character for when a PC bites the dust!
  The game could start out with an Alien attack on a town, so to begin with, no one has to be an XCOM member! After the fireworks die down, XCOM will come in, and recruit those who are of use, since it's a great way to keep them quiet!
   Once the players get involved with XCOM, one of them should be chosen to be the Commander (unless the DM decides to make the Commander an NPC under his control!). the Commander of XCOM should be the smartest, wisest most charismatic person available. When in doubt either chose the PC with the highest combination of Intelligence, Wisdom and Charisma, or roll a dice to decide! It's important to understand that bad decisions or poor performance will cause the Commander to loose his rank and be reduced to a lowly sargeant. So whoever plays the Commander should be aware that he has to fulfill his duties, its not about bossing folk around needlessly!
  Players should read the Base section, and order personnel and equipment as they see fit, although they don't have to get into every detail of base management and funding, equipment DOES come under the Players' control and they should see to it just as in any other campaign. The DM can add a special  NPC if he thinks the players need help: a Military Advisor. This person can suggest what may be better strategies, the best equipment etc, whenever the DM sees fit.
  The DM and Players should co-operate and decide which type of missions they preffer playing, what missions they'd LIKE to see, what items could be brought into the game etc etc. As always, player input is vital to a good AD&D game! :)

  XCOM is funded by numerous countries of the United Nations, they all have one aim: to stop the Aliens spreading terror or taking over the Earth. To that aim they fund XCOM. So now it's in YOUR hands to save the Earth, by slaughtering and capturing as many aliens as efficiently as possible, by whatever means are necessary! ;)
   There are only a few provisos: 
1) No one wants XCOM blowing the hell out of entire cities! Ergo they must rely on light infantry weapons. It may be possible in some missions (DM allowing) for XCOM squads to call down laser guided missiles, bombs or artillery on the enemy, but in general that's should be very rare. Since it's incredibly dangerous to the  XCOM personnel (near misses!); destructive of Alien technology that may be captured; and that XCOM (initially anyway) is very secretive and tries to keep the populace getting into a panic. Full scale wars attract attention!
2) You can't go round about killing off witnesses! That just causes more trouble, never mind moral and political problems. Bribery, threats or just plain helping folk in trouble should be adequate generally. While government agencies do get up to dirty tricks, XCOM is mostly made up of military personnel, who, contrary to popular belief, do NOT like civilians getting hurt!
3) However, traitors dealing with the Aliens are fair game! Espionage and intelligence is best handled subtly though, especially if public figures are manipulated by the enemy to be their spokesmen etc. 

 Research is vital to Earth's hopes to survive the Alien invasion! Further details can be found in the INFO section. Players who have a scientist or engineer can take these folk on missions, however, they are rarely combat personnel and getting such a valuable person killed would be a terrible waste!