Assuming you're on version 4 and self-hosted, the summary of the process is:
Move the contents of your installation directory to the root of your domain on your server. (Any questions on this I would suggest reaching out to your hosting provider)
Edit the URL in your conf_global.php file to reflect the file move in step 1. (depending on how old your community is this may be board_url or base_url)
Go to ACP -> System -> Support -> Something isn't working correctly to clear your cache.
Go to your Client Area ->Manage Purchases -> select your license -> scroll down to "Licensed URLs" -> click "Change URL." (this bit is the final piece to the puzzle to update your license URL on file)