Think ahead and write the move out notice before the minimum time period of which a landlord needs notice. For example, if there is a 30 day notice required, you want to get the move out notice in the landlord's hands no later than one month before your intended move out date.
Make it formal; grab a computer and create a letterhead with your name, address and contact information. Just below that, do the same with their name and contact information.
Write the move out notice; tell them what day you are moving out, what exact date that their rental will be vacant.
Get proof from the landlord that they have received the move out notice and that you will not be paying rent after that date. This may not be entirely necessary but if you feel as though you would like to cover your bases thoroughly (some people can be shiesty), it's not a bad idea to get them to sign a statement that they have received your move out notice.