Ask him on a date. If you ask about studying for finals together while on the date then that's a good way to make it ongoing, but go on a regular date first. Maybe make it very casual and go get something to eat together after work, like CF suggested.

There is no point in beating around the bush and acting like you just want to be friends - it only becomes complicated. If he's interested then there you go, if he's not then at least you know and you can set your sights elsewhere.

As to how to approach him - I'd just go with direct. I don't know what you work out or what kind of hours but, if it is appropriate, "Do you want to go get something to eat when we're done here?" is good.

Good luck.