How much notice to serve after section 21 issued

Tenancy Types and Management

We have a tenant who signed a section 21 whilst still on his first 6 months AST. I now want the tenant to leave the property. What is my next step? How much notice do I have to give him to leave? We let his AST continue on into a periodic agreement, but as I said he has signed a section 21 notice.
I find this all confusing, I very much doubt that he will pay the rent as soon as I ask him to leave so can I give him less than 2 months notice?
Has the notice got to be in writing or verbal and writing? Does he have to sign to say he accepts the notice?
Thank you.