Notice to vacate

Tenancy Types and Management

I know this is probably a really silly question (forgive me - i am new to this!), but here goes!
We have tenants whos agreements have expired. We are happy for them to stay on as rolling tenancies, but we do want to re-market the properties for better rentals. Once new tenants are found, what is the procedure for asking the current tenants to vacate? Bearing in mind they have never been a problem, we just need to acheive the best rental possible.
Any advice would be much appreciated.
Thanx, Angela.