Under a standard Assured Shorthold Tenancy Agreement you need to give your tenant 2 months notice to expire after a rent due date. The last point is important as it could mean almost 3 months notice would be required if you served notice the day after the rent due date.
To serve notice at the end or on a periodic tenant you would use a section 21 notice. Be aware though that there are two types of section 21 notice. One is for fixed term and the other for periodic tenancies.
If you are looking to serve notice during a fixed term for a breach of tenancy you would need to use a section 8 notice.
For more information and free advise on this please do not hesitate to get in touch.