DO give yourself some time
Some excellent advice I personally have received lately is to give yourself 3 days to process your feelings. Call out of work, miss a few classes, and enjoy some of the things that make you happy. Don't miss the important stuff, obviously, but there's nothing wrong with taking care of yourself in such a turbulent time.
DO spend time with friends and family
Use this time to reconnect with a group of friends you may not have spoken to in some time or, alternatively, plan to spend a day with your family. It is important now more than ever to surround yourself with people that care about you and that make you happy. You will have a newfound appreciation for your non-romantic relationships and it serves as a nice distraction from the situation at hand.
DON'T share personal information
Just because a relationship is over does not mean that anything you know about the other person should become public knowledge. It is important to remember that some information is told in confidence and that, even though the relationship is over, nobody wants their secrets made known to the world.
DO try to be friends, but not right away
Dating someone most likely means that, at one point, there was a good partnership created and without the pressure of romance a great friendship can bloom. However, it is important to give ample time before trying to take this step as things can get messy while the emotions are still fresh. On the other hand, there is nothing wrong with going your separate ways permanently.
DON'T do anything out of spite
It is easy to lose control in favor of emotions and try to get back at your former significant other in some way. It is unacceptable to take any negative actions towards them as, chances are, you will probably regret it. Additionally, this tarnishes any chance at a potential friendship and could ruin your relationship with any mutual friends. If it is not something you would want someone to do to you, it probably should not be done.
DO remember the good times
Try to remember the exciting and fun activities you shared in your past relationship. This can help stave off the negative thoughts or general sadness following a breakup, and even help you think of them as more of a friend. This step helps the most to contribute to the overall goal staying positive.