If you have been using cPanel with your previous host then you need to create a full backup of your account on the old server, then transfer the backup file via FTP from the old server to your new account. Please then inform us when this is done and we will restore your account from the backup provided by you.
If you were using another control panel then you need to download your website from the old server onto your local computer. Then you need to upload your files from your local computer to your new account which can be done via FTP.
Please email email@example.com if you have any further questions.