Copy the website from one webserver to another either through FTP or another protocol. (Install if necessary, or simply copy the files to the appropriate directory.) Backup your database if applicable and copy the backup across, then restore it onto a new database server.
Contact your new ISP and arrange for them to host your domain - it will take a day or two to have the pointers to your new isp propagate through the proxy servers of the world.
These are general instructions. Contact your new ISP. They will be able to give you specifics.
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