Are you starting fresh, meaning a whole new forum, or just moving what you already have to the new URL?
If it is a new install. remove what you already have. I would remove any add-ons first that you have put in to get it back to base. Then remove the software.
Go to your customer area and set the new URL for the license.
Then install it on the new URL.
Setup
If you are moving an existing forum.
change the license
install on the new URL
install any addons
The system should see the database if on the same server. May have to set the config for database communication
May have to copy your old database and put it on the server
Once everything is working delete the XF files from the old URL
At least this is how I remember doing it. Sometimes you can have your host copy all the files over to the new URL. Remember it it always a good idea to back up everything before moving forward.