Note- this process is NOT for upgrading an existing license with additional users, capabilities, etc. with the same Accoutn ID.

Preparation: 
Log onto the Security Console with SuperAdmin credentials. Use Setup  > License > Status to see the existing license information. If you are using an Evaluation license, make a note of the expiration date.
If you have any Replicas, verify that Replication is working.
Make sure you have a copy of the new Production license. Extract the .XML file from the .zip file

License uninstall:
From the Security Console - Setup - License - Status, then click on view installed licenses - click the license ID and choose Uninstall.  Check the yes, uninstall license box and click on uninstall license button.  Do not restart the server yet, install the new license right away.

Setup > Licenses  > Add new , point to the new license, Next, Install .

Once the new license has been installed, wait a couple minutes for the information to replicate to the Replicas (if any).
If you upgraded from an evaluation license to a production license, make sure you restart services before the evaluation license would have expired.  Applying the latest patch through the Operations Console is an excellent way to restart services, as it also patches the system.