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 files via FTP from the old server to your new account with JustHost. Please then inform them when this is done and they 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 into your Just Host account which can be done via FTP.