how would you transfer your website/domain from site to site?
Firstly take a full cPanel backup. Then upload the backup file to the new host cPanel. Then go to your domain registrar change the nameservers to the new host. Don't forget to delete your old hosting account or you will continue to be charged for it.
Sometimes, when you are transferring Word Press blogs you get an error while uploading the cPanel backup.
So what I do is:
Install WP on the new host. Download my Wp-Content folder from the old host and upload it to the new one via FTP.
Any other questions? Feel free to ask them.