Hello, gerisaunders, & welcome. First, you’ll need to go into the control panel for your domain that Godaddy provides & point the domain to the nameservers of whichever hosting provider you wish to use. Their knowledge base or customer service reps or the system information in their control panel should provide you w/that information.
Once that’s done, then you’ll likely need to get a search-&-replace tool to replace your current domain name w/the domain you wish to use instead. I personally like the one by interconnect/it, (https://interconnectit.com), but Google provides info on others as well.
Please remember that it may take 48 hours or even more for the DNS to propagate your nameserver changes, & attempts to work on or reach your website during that time may result in the site not being found or other behavior that seems flaky. Those problems should completely resolve once the DNS propagation has completed.
Please let us know if you feel you require additional assistance.