At GoDaddy

1. Add a new portal alias for the new location if the access address is going to change
2. Backup the database, download the file
3. Download all the files comprising the site.
4. Take note of the path of the site files (e.g  they are in a subdirectory)

At your new host

1. Set up a clean install of DNN using the same version of the core as your existing site. Make sure its in the same relative folder as the old. (This checks DNN can work at the new location)
2. Replace the database connection strings in the downloaded GoDaddy web.config with the ones of the working site you set up at the new host.
3. If possible stop public access to the new site.
4. Restore the database from the GoDaddy site to the new host overwriting the existing DB
5. Upload the site files to the new host overwriting the files already there.
6. Check the site operation at the new location
7. [EDIT]Change the SMTP settings so email is sent using your new hosts services [/EDIT]
8. change the DNS for the domain to the new location.
9. Have a coffee!

Some caveats on the above.  If there have been modification to the core or web.config specific to your old host, or you have custom modules, you could run into issues.

HTH

Antony