The steps to evict someone typically start with what is known as a Pay or Quit notice, giving the tenant a certain amount of time to remedy the problem. How much time the tenant is provided depends on what state this is taking place in. How this notice must be provided is also dependent on the laws of that particular state.
If the tenant fails to remedy the situation (in this case paying the rent), the next step is to file for the actual eviction through the local court system. A landlord cannot evict anyone; only a court can grant an actual eviction.
If you'll list what state this is taking place in, we'll get you information on the steps to do this.
Gail