Hi. I really want to move my current tenant out of the guesthouse. He never cleans and has an unsightly and dangerously huge pile of used computer parts, newspapers and old mail in the middle of the kitchen floor, despite being asked repeatedly to remove it. How much notice must I give him, and how must it be served? He has lived there more than one year. Thank you.

Different states require different amounts of days.

Here is a chart. I think it is up to date.
http://www.thelpa.com/free/statenoticechart.pdf

You need to use a form like this
Notice to quit Free Form (http://www.formsguru.com/forms/legal-forms/notquit.html)

I think you can hand him a copy and send a copy certified

Then if he isn't out in the specified time you need to go to the district court/magistrate

You really should check with your states law though in case you have to go through the court from the beginning or something.