Fine, I guess that was a little too simple. You need to work on your inner game because you haven't even said hi to this girl in 2 whole months. You haven't made any effort to approach her and you need to ask yourself why this is before you start asking
how to do it. I should also note that by focusing on this one girl you're putting too much value in her and it will cause you to make decisions based on your emotions rather than logic. You'll find yourself supplicating to her even though you know you shouldn't, and I know you will because I've seen it happen. Keep your wits about you so you don't fall into the trap.
You should read some material from around the forums and learn to apply it to your situation instead of looking for a quick fix, because it just doesn't work that way. I wrote some stuff on improving your inner game and included simple techniques which you can apply to a multitude of situations... including this girl at the gym. You can find it
here, and I highly recommend that you put some thought into why you haven't approached her yet. Approach anxiety is often caused by completely unfounded beliefs and while it is hard to overcome, the only fast way is to suck it up, stop giving a shit, be a man and just fucking do it.