First, you would get a new account with us - and then transfer all of your website files.

Once that is done, you would need to update your domain name's DNS/nameservers (with the company that registered your domain). That's all!

After your domain is completely pointing to your new hosting account, you could then safely cancel your webhosting plan with your old host.

We setup all accounts within 5 minutes of receiving payment (generally much sooner).
Once you've update your domain name's nameservers - it takes about 24-72 hours for your domain name to start working with your new hosting account.