Moving WordPress can be something WestHost can only minimally assist with -- so long as there are not a lot of custom details like themes, modules, etc. involved.
The quickest way is to log in to your WordPress admin ( domain.com/folder/wp-admin ) and change the domain in General Settings to the domain and directory path you require ( maybe domain.com/blog/ ).
Once that’s done, copy everything over from the folder to the new blog location, and click through to make sure it’s all working. Then remove the old folder and you’re set.
If you try to connect to update the URL for WordPress after you’ve moved the files from the original folder, it might not allow you to log in to the admin. If that’s the case, you can update the setting manually in the PHPMyAdmin >> WordPress database >> wp-options >> Home and URL lines 1 and 39. The changes in the database are immediate.