Getting the paperwork right when you sell a car is vital – otherwise, the change of ownership won’t be recorded correctly and you could still be liable for offences committed by the new owner.
This page on the Directgov website provides full instructions on what to do. You can also find instructions on the back of your car’s registration document (V5 or V5C).
I would strongly recommend completing the form with the buyer and then posting the torn-off section to the DVLA yourself – do not leave it to the buyer. The car is still your responsibility until the DVLA has been informed of a change of owner – so you should be the one to tell them.