If it is important that your site not experience any downtime, you should keep the service with your current provider until the transfer process is complete.
Once your site order has been filled, we will provide you with a temporary IP address so you can upload the site on our server (all email and web pages will still be accessed from your current site at this point).
Once you have uploaded your site you can update your domain registration to point your domain name to your new site. Contact your registrar to determine their transfer process, most have a web-based interface where you can easily make the update. You will need the names and addresses of our DNS Servers. If you wish to list us as Technical Contact for the domain, use "Techincal Support, email@example.com, 706-897-4743"
If you are unsure who your registrar is, lookup your registrar at Internic by entering your domain name, checking off "Domain" (not "Registrar"), and clicking "Submit". The "Referral URL" on the next page will usually take you to the home page of your registrar.
After updating the DNS Servers registered for your domain there is a 2-3 day propagation period where visitors could go to either site. At the end of the 2-3 days you should contact your previous host to have them delete your old site (perhaps first check your email there one last time by connecting to the POP Server = Your IP Address in case some email was delivered there during the DNS propagation).
There is also an extensive online manual available.
http://hostings.com 888-404-HOST (toll-free US/PR/VI/GU), 706-897-4743