[EDIT: Obviously, my domain name has changed and I’m on shared hosting now, but this still outlines the process. 2014-02-04]
Dynamic DNS is a system where you update the nameserver every time the IP address changes, so you don’t lose links.
I’m using freedns.afraid.org right now because it lets me use my own domain name (protichnoctem.com) for, well, free.
I set the nameservers in GoDaddy, then set cron to run wget every hour (of the “Direct URL” on this page)to update the nameservers with the current IP address. I know this is much more often than my IP address changes, but if it should change I’d like the domain name not to be broken for more than an hour (a cron wget is a fairly light task anyway).
If it works, I will be happy.