All I had to do was write a letter stating that I was gay, and handed it to my Commanding Officer. (I was an admin person, so the office was right next door.) I went through the proper channels first, though.
This works, it’s easy. The only downside, however, is that the DD-214 will say something like “homosexual admission” or “homosexual activity” as the reason for leaving. This is the thing that proves to employers I am in the navy, so if I ran into homophobic ones, then that would be an issue. However, once ENDA passes, this will no longer be an issue. (But then DADT will probably be reformed by then, as I expect it is more palatable to most people than ENDA.)
This is well worth doing! If you hate being in the military, do this. You’ll get an honorable discharge. You don’t need to prove that you are queer, you just need to say that you are. Visit the SLDN (Service Member’s Legal Defense Network) for more info.
You can call them if you are in trouble as well. They are very helpful.

