If you find yourself getting attached to someone soon after breaking up with someone else, this could be a rebound relationship. There are many people who have trouble avoiding rebound relationships because they may feel like they need to be with someone or need to feel loved. You really need to avoid getting involved with someone soon after breaking up, because you have not given yourself enough time to recover from your last.
There are supposed to be prescribed lengths of time to take off after break ups depending on how long you have been together, but the idea is let yourself get rid of any emotion or feelings you have from before. If you take these into your new relationship it will be like an anchor weighing you down and your new partner will suffer from it.
This is not to say that you can not date; that would be ok because you have to go on with your life. Just be careful about taking any relationship to the next level until you are really mentally prepared. One of the best things you can do is change your mindset. If you can keep yourself busy with family and friends this will help you take your mind off of your previous relationship. Get out and have fun, watch funny movies, laughter is good medicine for your health.
If you're feeling down at times its ok to talk to friends about how you are feeling. Getting it off your chest can help your healing process. If you can not let go of things maybe a little counseling will help you through.