I don't know how to get through the first room in the goron mines I can..

Walk to the left side and into the steel cage. Use your sword to break the wooden barricade and proceed forward. Break the wood barricade ahead; by now you should see the flame pillar blocking your path. Turn around and look for a button in the floor on the west side of the cage. Stand on top of it and equip the iron boots; this should deactivate the flame. Now unequipped the boots and run past the flame (it will only stay deactivated for a limited time).

To the left is another button. Equip the iron boots to deactivate the next flame. This time, run past the flame, then turn around and cross the bridge, passing the flame again (if you run out of time and don�t make it, there is a ladder to the east, climb it and jump back down to the button).

Climb the ladder ahead and jump to the next platform. Open the chest for 20 rupees. Now jump back and turn east. Jump across and turn south. There should be another button ahead. Use the iron boots to deactivate the flame blocking the path to the north. Run back across and past the flame before it reactivates (watch out for the slug just before the flame).

Follow the path around. Before jumping down to ground level, look north. You should see a small platform hanging out the side of the wall beside the door. Jump on it and equip the iron boots to lower it and unlock the door. Go through the door.

Once you're past the first fire jet, you may notice a walkway at the other side of the mesh. Go on the second fire jet switch and jump past it, then turn around and go back across the walkway before the fire jet comes back on. Climb up the ladder and continue back along the top of the mesh till you get to a platform that you can jump across to the other side. Keep going along that way and you'll get to the door to the next room.

Walk into the cage then use the iron boots on the switch on the left. Quickly run through and do a you turn. Then jump onto the next platform. If you have the hylian shield (which you can get fromm Malo Mart in Kakariko for 100 rupees) it will really help you. An octorock in the lave will be shooting flaming rocks at you. Lock on and use the shield attack on it to bounce it back at the octorock. Climb the ladder and jump over the lava to the other side. I think you hit a switch with iron boots on the right and then run all the way along the platform to the end and the door is on the right.
Hope this helps.

Climb up the mesh grate & jump to the otherside.