If you have broken up with your girlfriend and she claims she lives with you, even though she doesn't, you are well within your rights to evict her. If the lease is in your name, she is not legally a part of your household. Evicting an ex-girlfriend is less a matter of what to do and more a matter of what not to do. In emotional situations like this, it is easy to leave yourself wide open to civil or criminal charges, so it is important that you conduct yourself in a calm and logical manner.
Give her written notice that she is to leave your property at a certain time. This can be any time that you want, but it should be soon enough so that she has to take action, and far enough away so that she has time to pack her belongings. A day or two should suffice.
Agree on a time -- if you can -- when she can pack her things while you are out of the house. This will make the eviction process easier on both of you.
Change the locks. Once the deadline you've given her has passed, she has no right to be in the house without your permission. Changing the locks is the most effective way to make sure she leaves. Even if she's there when you change them, she will have no way to get back into the house when she leaves (and she'll have to leave at some point).
Leave her personal belongings alone. Do not put her things outside, as she can sue you if they are damaged or stolen.
Keep away from her. If you forcibly try to evict her you could end up with an assault conviction. This is why changing the locks is such a good way to deal with this situation.