If you're moving between cpanel servers it's very easy, or even just moving to a cpanel server from a plesk server is sometimes okay. Do you know which type/s you have?
Make a backup of your files and your database and then upload them to your new host. If you need help email me at globestar at rocketmail.com
Hm... as he said,do a backup of files... then transfer files to a new server... after that go to phpMyAdmin of your site and export database... then go on phpMyAdmin of your new website,create same db you had before and import the database...
Here's a step-by-step article for cPanel and phpMyAdmin and it's got a TON of screenshots for you: How To Move Wordpress To A New Server Or Host
1) Log into Cpanel 2) go to File manager 3) Compress the entire folder and download it to your PC / laptop 4) go to PhpMyadmin and select the database on which your WP website was working 5) Export the entire MySQL file 6) Log in to your new Cpanel 7) Upload the zip file and extract it 8) create a new database 9) Edit the Config.php with the new database details 10) Goto PHPmyadmin and select the new database , import the MySQL dump file into that Site is successfully transfered
i think the best way is full back up. than install the wordpress to new server and upload sql from cpanel.
backup all of your files. Upload to the new host. backup all of your database in MySQL (via phpmyadmin). Import the database to the new one. modify the config.php