What to do in each situation?

I've looked around and generally, it seems that if a guy gets dumped by a girl, his best bet in getting back together with the girl is to act okay and rarely talk to the girl (so she has a chance to miss him, I think). Is this true? Also, I know that this plan has chances of backfiring and the ex-girlfriend thinking he is not affected by the breakup so he doesn't really care about her and she gives up on him. What are the chances of the plan backfiring?
Also, I've been wondering about this plan and it seems it could work if the girl stays single after she breaks up with the guy, but what if the girl immediately finds a new guy, then what? Seems to me that executing the plan when the girl has a new guy would only get the girl to forget her ex easier. Maybe in this case the guy should keep in contact with the ex-girlfriend and execute the plan once she and her new man breaks up?

That is IF she and her new man break up
I think the best thing a guy can do after she dumps him is to find out WHY she dumped him. Maybe it's because of something he can and is willing to change for her? Some habit, some sentiments or the way he expresses those?

If it's a matter of no particular 'problem' I'm afraid there's not much a guy can do about being dumped..... except hope. Hope that she'll realize what she misses (or not).