Either give it to the hosting provider (they can do it fast) or : open it, there should be a folder (public_html) extract the files and upload them to the new account. If it has a mysql database then you'll need a full backup in order to get the mysql files. Create the new database and change all settings that are used to connect to it, after that run the .sql file with PhpMyAdmin. Hope this can help
From cpanel it is also possible to a direct restore for the gz file from bakup section... But then also anyway you need to create the database and db user id.