Ask the other person to move out. This can be a legal situation if your names are on the lease or you purchased the home in both your names. If the property is in your name then ask this person politely to find a new place to live.
Find another place to live. You may have to do this if your name is not on lease or title of the property. You also may need to move out if the other person becomes too confrontational after the break up. Finally, you may just need to be the bigger person and move on with your life. Ask your friends and relatives if you can stay with them or, if all else fails, just get a hotel room for a while.
Spend as much time away from home as possible. If there is no way you can find another place to live, simply stay at work longer or hang out with friends until you absolutely have to go home and deal with the other person.
Examine why the break up happened. If you do not learn from the past, you are doomed to repeat it. Just take a long last look at why the relationship ended and then move on with your life.
Talk to your friends and family about the breakup. If you keep your feelings bottled up, it could damage other parts of your life like work and school. Just tell these people about how you feel and what you are going through. If they are true friends, they will just listen and understand.
Go out and have fun with your friends. The best way to get over a break up is to get out and get on with your life. Go to the movies or your favorite club and just have a good time.
Stay away from the rebound relationship. Give yourself some time to get over the relationship. Besides, if you still live with the person you broke up with, bringing another person home could be awkward or even dangerous. Just concentrate on yourself and being happy for a while.