My son has a girlfriend that is living with us for a year now. I have asked her to live but she will not. Who can I get her out of my home? She pays nothing to live at my home.

Not sure what a "convickson" is do you mean a eviction ?
It is based on the law of your local area. Normally you are going to have to give them official notice ( often 30 to 60 days) and then if they are not out, you file for a eviction though the courts.

Living there a year, she has established residence and she has to be removed according to the local eviction process (ANY question on law needs to include your general locale as laws vary by area. ). This generally means giving her a 30 day written notice to vacate followed up by going to court for an eviction order if she doesn't.

Do you realize this might also cause your son to leave?