A rebound eh?
There are a few things you should find out before getting involved.
1. Why did they break up? She could be crazy, vindictive, unloyal, or unreliable. If she isn't, then her ex probably is.
2. Who is her ex and are you close with him? Surpressed angry feelings can linger long after the break-up. Last thing you want is a fight with her ex.
3. Is she your type? People with nothing in common don't usually have a lot of fun together doing things the other person has no interest in. She might also be open to new things.
4. Is there someone else? Better hope there isn't.
Being nervous around someone you like is normal. Everyone usually is. I'm guessing you go to school with her? You're probably no stranger to her if she's one of your classmates, I would just go up and tell her I heard the news about her breakup and that I'm sorry it didn't work out. She will either respond with sadness, anger, or with a total care-free reply. Her response will tell you a lot about the circumstances of her breakup and relationship but you don't care, you just want to break the ice. Tell her it's none of your business, but ask what happend. She will either tell you or she wont, that doesn't matter either. Just tell her you hope she's feeling ok and that you're around to talk if she wants.
Dont expect her to drop into a new relationship with you right away. If she seems like she does, it's not good. Despite your excitement, that shows shes not taking things seriously and she's looking for a new bf for a particular reason - a reason at your expense. If she can drop her ex and immediately get a new bf, what does that say about a future with her? Be a good friend to her and be yourself. Eventually, after a few weeks of getting to know her, ask her if she'd like to do something sometime with you. Don't wait too long or you'll miss the oppertunity and be stuck in the friend zone. Being her friend has its benefits, but do you want something more? You will have to work up that courage to be yourself and make her laugh and smile. Be there for her when no one else is.