Things are not working out. You want her to move out. This is a tricky situation that needs to be handled with tact and diplomacy. There may actually be two tasks you must accomplish: breaking up with a girlfriend and evicting her. Even if you do not want to break up with her, you are terminating a part of your relationship and this must be handled with sensitivity. If children are involved you must be sensitive to those needs while still holding boundaries. Although most states only define your girlfriend as your tenant if she has been paying rent, do not assume this is the case.
Talk to her. This is the most straightforward, honest approach and the path of least resistance. Sit her down and explain to her that things are not working out, you cannot live with her any longer and you want her to move out. When discussing options with her give her a few choices to ease the pain of the situation, but do not leave the terms of when and how she leaves open-ended or she may never leave. Say to her something like, "I understand that this may be hard for you but I think it's best that we get some closure rather than leaving the arrangements open. Do you think you can be out by the end of the month?" That should leave enough time to get a new place. Set a time limit for the discussion, about a half-hour. Discussions longer than this will just escalate into arguments or crying spells. Remain calm and, if necessary, have a friend that you can talk to at the end of the half-hour. It is best to have this discussion in a public place on neutral turf.
Listen to her but hold boundaries. If she asks for six months, say no. If she asks for a month and a half, say yes. If she agrees to a month and a half and she has not started packing her stuff by the end of the first month, get some boxes from the grocery store and offer to put her items in these. Appeal to her family if necessary. They may be able to talk some reason into her. If children are involved, try to be understanding but do not let her use the children to manipulate you. If they are your children make formal financial support arrangements and work out a visitation schedule. Remain emotionally detached. While she may resent this approach and try to continue to emotionally connect with you, this is not healthy for either of you in the long run and will only lead to false hopes. If you are also breaking up with her as a girlfriend, do not continue to be physical with her and do not put yourself in situations where this is likely to occur.
Get a lawyer. If the agreed-upon time to vacate has come and gone, get a lawyer. If you have an Employee Assistance Program through work, many of these programs offer an initial free consultation. A lawyer will be much more helpful than the police, who will likely say they can do nothing if she wants to stay -- it's a civil rather than a criminal matter. If she has been paying rent, she is legally a tenant and formal eviction proceedings must commence. Although states differ, all require notice to be given formally to evict a tenant, whether or not she is your girlfriend. Tenants have many protections under the law and any mistakes you make can be costly. You can serve a nonpayment notice if she has been paying rent and this has lapsed. There are also conditional or unconditional notices you can give, which basically give the tenant a certain number of days before further legal proceedings can be initiated. If you have not given notice, you cannot legally proceed with an eviction.
Learn from the experience. If living with her was making you unhappy, perhaps she was unhappy too. When a relationship is limiting, both parties tend to feel positive after a period of mourning has ended. If you are also breaking up with her, take your time to really get to know someone new when you are ready to start a new relationship. Do not let future girlfriends move in with you unless you get them to sign a lease. If you set appropriate boundaries at the beginning of the relationship, it will be easier to maintain them and your relationship just may be happier. Think hard about what you want in a relationship and wait to move in with someone you feel could be a long-term partner to you.