How to transfer your website to another host?

1. Find a new hosting provider and purchase a hosting account 
2. Backup your database and FTP it to your development PC or your home PC 
3. Upload your website to the new hosting account. check that it works as expected by surfing to the IP
4. Create a database with the same name as your old database and the restore it using the backup file. 
5. Login to your domain name account and change the nameservers over to your new hosting company
6. It normally takes 24-48hrs for the nameservers to update, once they do your website will automatically be served up from your new hosting company

Ideally you should stop your website until the nameservers update so that the database maintains its integrity.