It varies a little depending on where you want the changes to be reflected, but in many cases, people use (free for personal use) services such as DynDNS or No-IP, which come with what is known as "update clients" that perform the task you're describing.
So, as an example, say that you sign up with No-IP; you'd have an address such as "myhouse.no-ip.com" which is kept up to date automatically with their update client.