How long have they known each other for?
How many times have they seen each other?
It really depends on what has been going on so far. It sounds like he doesn't know if she likes him but he likes her a lot, right?
I'll give a general advice as I don't know the whole situation. ie. her past relationships, how she feels about him, what they have done, what feelings are there...etc...
what's the best way to tell a woman that you're interested in her?
I find that the straightforward, honest approach works well with me. If you really like someone, you've got to tell that person your feelings or else it can be too late. She could be moving, find someone else, become more busy, etc. A guy must tell his feelings from his heart and they must be genuine. He could also suggest giving this "dating" thing a try and see how it goes. Don't put any pressure on her. Give her the space and time to think things through.
I hope that she is interested in him as well, but if she isn't, she may start to warm up to that possibility. Girls like to know that someone is interested in her. It's the feeling of being needed and wanted that makes them feel special. This feeling is important, well, at least for me.
I hope this helps. I'll try to write more later. Gotta go.