After defeating Bahamut and gaining him as a GF, leave and head back to the Ragnarok. Talk to a party member then talk to Irvine and land at the Deep Sea Research Center again, inside you will see the core has been destroyed, a Save Point and a small bridge. Cross the bridge to climb onto the pillar and head down to the room below.
Here you have to solve a puzzle to descend further; how this is done depends on whether Zell is in your party. Each floor will be explained for both solutions, the goal is to get to the Excavation Site with 10 units of steam left but you need to use these units to open doors.
Floor 1: Draw Point for Dispel can be found here.
With Zell:
Talk to Zell, he will see a machine and Squall will check it out. You will use 4 units here.
Without Zell:
Talk to the party member near the hatch in the floor who will see a machine which Squall will check out. You will use 4 units here.
Either way, once the door is open, head down to the next level (The way down is on the left side, if you approach from any other side you will just walk away from it)