Generally, the procedure you will follow is something like this:
1. Set up Web hosting on your new service provider. (Note: Web hosting and domain registration are two different things. You will not register your domain at your new provider, nor transfer your existing domain to your new provider yet. You'll buy a Web hosting package, but that's all for the first step.)
2. Upload your Web site files to your new Web hosting package. The new hosting package has no name yet, so you have to upload it using the IP address rather than using
www.yourdomain.com or whatever.
3. Once the files are uploaded to your new site, you will either instruct your existing domain name registrar to change your domain name to point to the new site--or, if you have access to the DNS records for your domain name, you can change it yourself.
After you do step 3, there will be a period of time--usually 24-48 hours--while the rest of the Internet becomes aware of the changes. During that period of time, some people who go to your Web site will see the old server, and some people will see the new server.
4. When the changes have propagated, which will usually be in 48 hours or less, you tell your old Web host to cancel your hosting account.
If you want to, you can also transfer the domain name registration from the old service provider to the new service provider as well. This is not necessary; the hosting and name registration are separate things. You can do it if you like, though, or if you don't trust your old service provider. (I generally like to keep all my domain names registered at the same place as my hosting is done.)
