Summarize the following:
Before you make any moves to reach out to your ex, make sure she's available and that you really have her best interests at heart. If she's dating someone else, don't try to come crashing in on the relationship. Wait until she's not seeing someone. If you truly care about her and her happiness, put aside any jealousy, resentment, or bitterness before trying to approach her again. If you know your intentions are good and if you're on good terms with her friends, you might consider recruiting their help. But proceed cautiously--this can backfire in a big way if her friends decide to speak up against you rather than for you. If you can get the help of her friends, though, they can be invaluable allies in helping your cause. When you've taken enough time apart and are ready to try reaching out to her, do so in a low-pressure way. Don't start off in an emotionally-loaded way by saying something like, "I really want us to get back together" or the dreaded "we need to talk." Make it clear that you only want to get together as friends to check in on each other's lives, not to make a desperate attempt at reconciliation or hash out past grievances. Set up a meeting in a neutral, low-pressure space. Suggest getting lunch or a cup of coffee. Avoid choosing a location that's emotionally charged for the two of you, like a cafe you used to frequent together or the restaurant you went to for your first date. It might seem like a clever move, but it will just taint the encounter and be more likely to put her on the defensive from the start. If your first meetup goes well and you're both amenable to meeting up again, aim for a similarly low-pressure situation. Make it clear that you're interested in reconnecting as friends at this point and that you're not expecting this to mean that you're back together. If, after spending some no-pressure time together, you both mutually feel that there's still a strong connection between you, you can bring up the topic of your relationship and whether the two of you might want to explore the possibility of getting back together. You might say something like, "I've been thinking about our breakup, and I think I understand the problems that led up to it. Do you want to talk about it?" If she reacts negatively to this suggestion, back off. The harder you push when she's not receptive, the more you'll hurt your own cause. Give it some more time and re-address the topic if she seems more receptive. If she still isn't into it, start to reconcile yourself to the possibility that it may just not happen.

Summary:
Do the right thing. Network. Start slow. Keep things casual.