I would say, green screen or cgi the submarine exterior, then just make a set for the interior of the submarine.

Thanks for the tips, but I was looking for more of a "Green Screen Model" effect. Does anyone know how to layer something over the footage to add the look of under water?

it depends how deep you want the sub to look.

if its shallow water then you might see some of the "caustics" which look like rippling light beams moving across the bottom of a swimming pool. Then do those using an effects package.

If the sub is in much deeper water, then you don't see the caustics. What you do see, is a softness and a very shallow depth of field due to dark conditions and particles in the water. You will have very diffuse light coming only from above. On the film "The Abyss" this was achieved by filming the model in a dark studio with lights above, and a few seconds before rolling the camera, they released some smoke to give a soft diffuse particle look.

Yeah, this tutorial here covered it pretty nicely for me, it gives the basic gist of setting up an underwater scene.

Yes, actually, that's how I made the underwater effect I did in my signature. I changed some of the stuff to make it fit my scene better, but yeah, that's how I figured out how to do underwater scenes.