How do you go on a date with a gay guy in the closet?

This would really depend on how willing you are to make it obvious you are on a date. You could go to the movies, out to eat somewhere, and still look like two buddies just out doing stuff. For something a little more romantic, you could do something more private- a nice dinner or movie at home, or a long drive into the country and... I dunno, a picnic? That kind of thing.

It really just depends on what you would call a date. If you two talk about it, I'm sure you could find something you could both do that would feel date-like enough, and allow him to stay publicly in the closet if that's necessary. You won't be able to do everything you might want to, but work at it and you can find something I'll bet.