Goma Cave is located to the North-east of Vault, so head across the bridge and the start moving north. If you run into Lunpa, just go back to Vault and start out moving east first. This is the first dungeon-type area that one encounters (aside from Sol Sanctum, which is really far too simple to be considered a dungeon.) in the game. It isn't that much more difficult than Sol Sanctum, but there are numerous different challenges here.
Outside the Cave
Jump across the broken bridge and push the tree stump out of the way until you can climb the ladder. Head right, then use Move to pull the next stump into a pit so that you can cross. Climb the next ladder and head back to the left until you see a stump covered in leaves. Try to use Move on it; it won't work, so cancel the skill. When this happens, Garet will come out and start talking. At this point, Ivan will appear and use Whirlwind to move the leaves off of it. After a short cutscene, Ivan will rejoin your party. Now, you can Move the stump out of the way. Push it into the water, jump across to where it was, and then use Whirlwind on the leaves stuck to the wall to reveal a hidden path. Enter it to explore Goma Cave.
Inside the Cave
Once inside, just move straight north until you find a spot to jump across the water. Then, when on the other side of the river, head south until you see a set of stairs. Ascend them and enter the door at the top.
First things first, head right until you see another stump with a wide range to move. Push it Northeast until it clicks into place. You can see a Djinni from here; pushing this stump will enable you to reach it later. Move back to the left along the southern wall until you see a spot where you can jump across a short watery area. Then go through the door on the other side. On this floor, head as far left as possible until you reach the end. You should see a platform in the water to jump across; take this to reach the other shore and then head north until you see a set of stairs going up. Taking them will return you to the previous floor, except you will now be on level with the platforms that were formerly outside of your reach. Walk north, then use Move to push the stump so that you can stand on that platform. Jump south onto a new, wider platform. Walk as far south as you can on this platform and push the stump on a nearby platform off the edge. It will fall off the map and into the floor below. Head back north to the edge of this platform, but instead of returning to the stairs, push the first stump to its original position, and jump to the left to get the treasure chest (It contains a Lucky Medal, which will come in handy later.) Return to the wide platform and use the same technique as before to reach the stairs you took to get up here. Go back down to the previous floor.
The stump that you just pushed off onto this lower floor has opened a new path. Jump south and then to the left to see a new set of stairs going up. These will take you to the platform near the Djinni. Jump across the stump you locked into place first to reach the Djinni. Talking to it will start a battle. You must defeat it in order to obtain it. Have Garet physically attack, because his fire Psynergy will be worthless against it (After all, it is a Mars Djinni.) but earth and wind techniques will still be adequate. Once you have defeated it, the Mars Djinni Forge will join the first character in your party lineup that currently does not have a Djinni. Note that each character must have an equal number of Djinn whenever possible; you cannot have Isaac with both and give none to Garet and Ivan. For now, it will be best to keep like elements together, so leave Flint on Isaac and set Forge to Garet. Go back to the other side of the platform (across the stump again) and take the staircase leading up. Head north until you run into another stump blocking your path; you know the drill by now, just move it off the edge and it will fall into the water. It will create a path heading left, but you should ignore it and continue north. Pass through the door, travel right across a bridge, and then head through an exit on the south side of the cave. Outside, you will see the town of Bilibin.