You need to do the following steps:
Step 1: Download all files from your server to your computer. Be sure to keep the folder structure.
Step 2: Create a database backup using a tool like phpMyAdmin and save it to your computer.
Step 3: Upload all files from your computer to you new server. Remember to set the appropriate permissions.
Step 4: Create a database on your new server and upload your backup using phpMyAdmin.
Step 5: Change all relevant lines in configuration.php. These lines may include: $mosConfig_host, $mosConfig_user, $mosConfig_password, $mosConfig_db, $mosConfig_absolute_path, $mosConfig_live_site and $mosConfig_cache_path.