If your website doesn't use MySQL databases, you will only have to upload your files to our server - find a tutorial here :)
Now, if you have a PHP based website, check if it has any configuration files where domain name or path to the files can be set. Update these values if needed.
And if your website is using MySQL databases, you will need to:
Backup database on the old server. You can find a detailed tutorial here.
Create a database on our system, before you can restore a database backup.
Import database backup to our server - click here to find a tutorial.
And finally, update configuration files. When the database is restored, you will need to open the configuration file of your PHP script and update MySQL database details.