I have a tenant that has never paid their rent on time, have to ask several times. They harassed the upstairs tenants to a point that they asked to break their lease. They were very good tenants and I hated to see them move. I informed the downstairs tenants that their lease was up on June 30, 2013 and that I would not be renewing the lease. They now are refusing to pay May's rent. I had them served with a 3 day notice to pay on May 15th... now what do I do?

First - is his lease really up on June 30?
If so, go to your local courthouse and file eviction papers. Be prepared for a possible hassle, so make sure all your ducks are in a row. Hire a lawyer if he starts finding reasons to fight eviction. Some people do find obscure legalities or ways to delay. It sounds like he plans to not pay either May or June if he can get away with staying there that long, which he might.

You go to your local housing court and file for an eviction order. You should have done that on May 16.

Why did you let the good tenants go and not terminate the bad ones?