If you've just installed, and it says it's expired, or say it has any amount of time less than a year, what has happened is the install has found an old expired product key, and decided to use that instead of prompting you for a new one. You need to tell it the new one:

 Open Norton Protection Center. Choose 'Help and Support' in the top right. You may have to select 'One Click Support'.

When 'Help & Support' window opens, choose 'Activation' in the top right.

When the 'Activation Status' window opens, choose 'Next'. Input your product key.

Finish the activation, and it should be showing a year until it expires.

 Nore that if you've purchased a product that can be installed on multiple computers, like Norton Internet Security, the clock starts ticking on the first install for all computers. If you install it two months later on a second computer, you only get ten months on that computer.