When you have purchased a renewal code, you go into your Avid account (www.avid.com/account), log in with email/password and click on View My Products and then on the black bar with the product name (e.g. Sibelius or Pro Tools).

On the right of the screen you can see the start and end date of your current license. Enter the Renewal code you have been sent in the field "OR, for renewal purchases made through your Avid Reseller" and click on the blue arrow.
The license is then updated with a new period.