In order to obtain the second stone, you must defeat the monsters inhabiting Dodongo's Cavern. One of the very first enemies that you will run into will be a Watcher. These can be defeated by a bomb or a Bomb Flower. At the beginning of the cavern, you will not yet have bombs, so you will have to rely upon the Bomb Flowers. There is another use for the Bomb Flowers in Dodongo's Cavern - there are some strange-looking walls throughout the cavern (you will probably know them when you see them) which you can detonate a Bomb Flower or a bomb in front of to reveal passages behind them.
You should now have pretty good skills in the game, so I will not insult you by providing a walk-through which contains painfully obvious things in it. Instead, I will focus on the areas and the enemies that are more problematic. At one point, there will be a switch on the floor which opens a door when you step on it, but the door closes once you get off the switch. To solve this problem, pull one of the nearby statues onto the switch to hold the door open. You will have to use this strategy a few more times in the Dodongo's Cavern. In another part of this stage, you will encounter fire-breathing dinosaurs about the size of your character. You must sneak behind these dinosaurs and strike them on the tail with your sword to damage them.
In this same room, when you defeat all of the dinosaurs, you will notice many unlit torches. Use a Deku Stick to transfer the fire from the lit torch to all of the unlit ones. This will open the door at the end of the long corridor. I believe that you will encounter sword-wielding dinosaurs in the very next room. These are very challenging enemies. I find that it is best to Z-target these enemies, and then to deliver a jumping-swinging-sword blow to them (I think that this is accomplished by holding the joystick forward and pressing the "A" button while Z-targeting).
It will be a while before you finish them off, for they will retreat before they are dead and allow their friends to renew the attack. In a different room, you will see a mound surrounded by 4 statues. If you attack the statues with your sword, however, they will come alive. Lure each statue out of its original spot until you find the ladder that was hidden behind one of the statues. Climb the ladder, step on the switch, and continue walking through the level. Now, in another room of this level, you will see a lot of Bomb Flowers gathered around what appears to be a stone wall that is jutting out into the room. It turns out that this is actually a very large stone staircase. In order to lower the stairs, you must place a Bomb Flower (not a flower in-line with the other ones - get a flower near one of the doorways) in the small gap where it appears that a Bomb Flower is missing. If the bomb is correctly placed, it will start a massive chain explosion which will result in the lowering of the large stone staircase - allowing access to the upper portions of Dodongo's Cavern.
There is another problematic area in one of the upper parts of the level. There will be a large bonfire blocking your path, and there will appear to be no way around it. There should be a diamond-shaped stone on the wall directly above the doorway. Use your slingshot to fire a Deku Seed into the middle of the rock. The bonfire will temporarily lower, allowing you to pass. There is another room similar to this, with the exception that there are two bonfires. Lower the first bonfire in the manner discussed a few sentences ago. However, to lower the 2nd bonfire, you must turn to the left and fire a seed in the now-exposed 2nd diamond-shaped stone (this all must be done rather quickly or the bonfire will begin to burn again). After passing these puzzles, you should soon find the bombs in a treasure chest. Bombs are very useful throughout the game and are essential to both find and defeat the leader of Dodongo's Cavern. After you find the bombs, jump down onto the huge white dinosaur skull located in the main room of this level. Place a bomb in each of the "eyes" of the skull, and the eyes will glow red.
When both eyes are glowing red, the mouth of the skull will open, allowing you access to the final parts of the dungeon. There will be a switch in the middle of the floor in the next room, but it seems that there is nothing to depress the switch with. If you explore the paths leading off to the next room, however, you will eventually find a block then you can haul back to the first room. Push the block onto the switch, and go through the doorway that opens. This will lead to what appears to be yet another dead-end. You will notice a large crack in the floor, though. Place a bomb on the crack and you will create the final "doorway" which leads to the leader of Dodongo's Cavern - Dodongo himself (surprisingly). This behemoth is actually not very difficult with the proper equipment and strategy. First, make sure that the Hylian Shield is equipped and that the bombs are equipped with your "C" buttons. Now, raise a bomb above your head and approach the dinosaur. When you come close enough, it will open its mouth to prepare to spew flame at you. If you time it right, you should be able to throw the bomb right into its mouth. When the bomb explodes in its stomach, the dinosaur will be knocked prone to the ground.
While it is in this prostrate position, hack at it with your sword. When the dinosaur recovers, run into one of the corners and duck and cover by hefting the Hylian Shield. Doing this should protect you when the dinosaur attempts to roll over you. After it rolls by you, it will get on all fours again. Just repeat this same procedure all over again until you defeat the dinosaur. Then find and recover the Heart Container (NEVER forget this) and exit via the glowing light. When you exit, you will meet Darunia outside of Dodongo's Cavern. He will be elated and will hand over the 2nd stone to you, and he will give you advice - to go to the top of Death Mountain to seek help there. More information will be found under "Fairy of Power" in the "Fairies" summary. After finding the Fairy of Power, your next stop should be to the home of the Zora's, which is in the next section…
Proceed to Zora's Domain...