Once you reach the area Beneath the Base via the link elevator, you'll need to burn away the ivy, proceed down to find a massive chasm. Along the left wall is a massive circular door lit by spotlights. Open this door to access the submarine. The door needs a handle and stone glyphs to operate.
The five glyphs are found on the way down to this cavern. There is a short path on the left that leads to a statue, the glyphs are at the base. Once you leave the chamber with the large reptilian statue in the center you'll head down a path lit by blue crystals. The path is at the third set of crystals and directly opposite the breakable wall.
Continue down into a large chasm. The handle is found in a stone sarcophagus on the right side of the tree in the center of the chasm. Look below the shaft of light coming through the ceiling to find this tree. You'll have to walk around to the left a while to find the entrance. On the other side of the same tree is a carved inscription that instructs you on the correct placement of the glyphs. You'll see a vision/memory after which you click on the stone drawing to obtain a copy.
Travel back past the large circular door to find a small circular area surrounded by pillars and small statues. Insert the handle to the box on the left and the glyphs on the right. I think the order is the same for everyone? If you number the holes in the box 1-5 and the glyphs 1-5 reading gown, then my order was.
Glyph 1 - slot 1
Glyph 2 - slot 5
Glyph 3 - slot 4
Glyph 4 - slot 2
Glyph 5 - slot 3
Turn the handle behind you, walk up to the large circular door and step on the pressure plate in front. The submarine is basically straight in front of you after a short walk.