You’ll start off on the outside deck of the Highwind. You can go down the ladder to go into the Northern Cave or go back to the cockpit to return to the World Map. To continue, choose to go down and when you jump into the crater descent, you will see a treasure chest with a Save Crystal in it. You can use this to create a save point in the Cave, but you can only use it once, so don’t use it yet. Next to the treasure chest is a door or a cave leading back to the Highwind in case you need anything or just running low on supplies.
Go down the path, jumping across the gaps automatically. You can pick up the Guard Source in the chest along here. Leave the descent and you’ll enter a new area. Here you can climb down the grey areas with O. Climb down the right side and get to the chest with another Guard Source in. Go to the next chest (Mind Source), don’t walk off the edge of the ledge below or you’ll have to climb back up. You can now either climb back up and get the rest of the chests, or continue down into the Cave. To get the chests, firstly climb up the ledge to your left. Go all the way to the left and climb up two ledges, then walk to the right to find another chest containing a Magic Source. Go left again, go up to the next ledge, then go to the right and climb up again. Walk all the way to the right, climb up again and head left to find a chest holding an Elixir.
Then go up to the next ledge, go left, and climb up the grey part to get to a chest containing a Power Source. Go to the right and past a large rock to obtain a HP Absorb materia. When you’ve got all that, jump back down, go right, and climb up the ledge to reach the top again and make your way south to an area with a load of ledges again. Go to the right to fall down and go to a hidden chest on the left with a Mind Source in. Go to the ledge edge and press O when the message appears to jump up. Walk left until you fall down, then go right and walk through the doorway by pressing up. Through here is a chest with a Megalixir.
Make your way back to the other screen and go to the left to fall down another level. Get the chest to the right (Hero Drink) and go through the doorway on the left. Get the Guard Source and follow the path to a Power Source. Go back out and go up to the opening that will take you back to the top. Go all the way down by running right, fall down, right again and go through the doorway. Go through the opening it takes you to, and go left, then fall down and then right. In the next screen climb down the first “ladder” and here’s a good point to use your Save Crystal. Then climb down again and you’ll meet the rest of your friends. You need to decide which way they should all take, left or right. Choose a way for Cloud to go and then tell the people you want in your party to go the same way. If you told the people who were in your party before to go another way to Cloud, you’ll have to make a new party.
I’ve separated the paths: right path, and left path, with the upper and lower routes separated.