Break ups are definitely no fun for both parties involved. One of the most important things for you to come the realization is being comfortable with yourself again and not having a dependency to just jump right back into another relationship until you have had enough alone time. You have to get your head cleared even if you are getting out of a relationship to be with another person. You should have enough respect for your last partner to settle your differences with them and let the wounds heal a bit before you just jump in head first to another one. People are always making this mistake and end up paying for it in the long run. I would recommend that you spend some time with your friends especially the ones that you might have pushed away when you were together with your last partner.
One of the other hard things for people after a break up is investing the time to learn about another person and getting back into the dating scene. I seriously recommend you spend a few weeks or months being single again and enjoying yourself, family and friends. Once you are comfortable with your status of being single you will see that you will have opportunities all around you to meet new people. You can try online dating if you are trying to meet someone outside of your immediate circle of friends or the bar scene if you want to keep it casual. Church is also a good place to meet singles if you are at all religious. If you are a guy then you might want to try some Salsa or Swing dance classes as there is usually about a 4-to-1 ratio of women to men. If you are a pet lover then there are tons of singles that walk their pets in dog parks and to dog friendly eateries. Pets can be an easy conversation ice breaker if you have any issues with approaching strangers. If you are into sports and outdoor activities then get involved in league play where there are big groups of players like softball, bowling or volleyball.