I was in a seriouse relationship for 2 1/2 years and them my girlfriend broke up with me. I'm 19 and she was my first everything. I know the only way I'll ever get over her is to start dating others. I have noticed a couple girls look at me and make eye contact but I don't know how to approach them its been so long... any tips or advice?

How long ago did you split up? If its recently then don't just go rushing in to dating again if your not ready.and no its not the only way to get over her,you need time to get over her,not jumping head first in to another,the only thing that brings is hurt to the person you start dating when you realised you rushed in to it and was wrong for getting in to another so soon

It takes time to heal,not anew girl on your arm

Well its been about a month now

Wait and see if the other person takes action. Clock them and see if they look at you when you're near them, if so walk up to them and say anything like hi and start taking about anything. Once you've done it once every time after that will be easy.

I know the only way I'll ever get over her is to start dating others.
That's not entirely true, as first you must heal, and get over the ex to the point of being able to have fun with others, without her ghost haunting you, and making you miserable. Having said that, don't let a fear of rejection, stop you from introducing yourself to strange females, and going from there. Confidence is the key, and courage is all you need. Just like Nike, just do it. If she rejects you, so what, not meant for you. There will be others don't worry.

does it mater much that I'm "on the rebound"?
Yes it does, as using someone to get over your own hurt feelings, is not fair to them, and a low down selfish a$$ way to feel better. Better you heal, and then be real.

I took this from your other duplicate post, because it was a good concern, to be addressed.