For some reason, we see divorce as a signal of failure, despite the fact that each of us has a right, and an obligation, to rectify any other mistake we make in life.
A divorce is certainly not the end of your world, not even close to an end. It is only the end of a relationship. Only because it's called a divorce, and that it requires the approval of a court, shouldn't make you believe it's anything more than a breakup. I'm not saying it's just as easy, I'm saying technically it's just that. For whatever reasons it happened, it did. You have two options now. Sit contemplating on it or move on to a happier, better tomorrow. If someone asks you out, there is no harm in considering it as a potential tomorrow. But if you're finding it difficult to mentally agree with yourself, this advice should come handy.
Guide the Guilt
Though coping with divorce is rather difficult, the first thing you need to do is to not feel guilty about dating someone else. Guide the guilt out as soon as possible as this is perfectly normal. You are no more in a relationship, and should thus, not have any emotional liabilities.
Keep telling yourself how beautiful/handsome you are and how you deserve to be loved. Be confident of yourself and don't consider the divorce your failure. You have nothing to feel bad about. In fact, you had the strength to start over; feel proud about it. A confident person is always attractive.
Make sure your past is sorted. If your ex-spouse and you are still fighting and are in regular touch, you should consider waiting till both of you move on. Don't let problems from your past affect your future. If you have children who are old enough to understand dating, discuss the possibility of you dating someone with them. This will make it easier for you to deal with the situation.
Bygones are Bygones
Don't look at future prospects through your old relationships. Don't compare. Just because one relationship did not work out, doesn't mean none of them will. Always be approachable and understand the difference between your past and present. Living in the past will keep you there and it will be impossible to move on. Every person is different; treat them different.
It is a therapy, really. Buy yourself new clothes and style yourself completely different. Discover a new you. If you have the money, get yourself a makeover. You will be more confident about yourself. Looking great does increase confidence after all. Shop till you drop.
If none of this still helps, go on a small vacation. Deal with your thoughts properly, sort them out, and come back feeling better. Once you've given a closure to all your emotions, you will find it very easy to start afresh.