No problem, its easy, and can be done without having any downtime for your site at all.
What you would want to do is first set up an account with us. We'll set up the account then mail you a welcome letter after you sign up. You can then upload your files, using the ip address to get it all working, set up email addresses, etc. Then, when its all 100% ready, you can change the DNS name server info for your domain to the ones for our hosting service (they are mentioned in your welcome letter) and then in 24-72 hours your domain should switch over and start working on our servers.
We're here for you every step of the way, just ask if you get stuck at all.