Let's take a moment to define what is meant by 'rebound relationship'. A rebound relationship is the first relationship you enter into after a breakup, and it typically happens rather quickly to fill an emotional void. Technically, any relationship after a breakup, no matter how much time has passed, could be a rebound.
There are many reasons for breaking up, and you need to take an honest look at what led to your previous relationship coming to an end. The key here is to be gut-wrenchingly honest with yourself. This will help you to avoid being with someone who has the same problems as your ex. It will also help to prevent you from making the same personal mistakes that contributed to your prior breakup.
While it takes two people to ultimately cause a breakup, you may feel as though your partner was largely to blame. If that's the case, then it can be very difficult to trust somebody new. Do your best to remember that the new person in your life is not the same person as your ex. If you do a good job of avoiding past mistakes, then you should have picked someone who is different from your ex anyway.
Of course this is one of those things that's easier said than done. After all, you are most likely attracted to a certain type of person for a reason, good or bad. In other words, while there may be positive aspects that you respond to, there are also negative aspects that are alluring in their own way. Therefore, you need to be on your guard so you don't let the "good stuff" overpower the "bad stuff". Now, that doesn't mean you have to find somebody who is perfect, but you should do your best to avoid the bad stuff that led you to looking at a rebound relationship.
As you are starting the new relationship, avoid the temptation of spilling your guts about why you are on the rebound. This is especially important during the first few dates. Over time, you may want to reveal some of what went wrong, but only if it's relevant to the conversation, or if it's to help explain something about you. For example, if after a month or so, your new partner mentions that you seem to have trust issues, then you can explain why that is, and how your previous relationship contributed to the problem. The one thing you don't want to do, however, is have your old relationship sabotage your current one.
How a rebound relationship can work will depend on how well you are able to put the past into perspective. The main thing to keep in mind is that they really can work.