To keep up the fast-change routine of frequently refreshing DNS records, you need a couple of things. First, a provider. This is "yourdnshost.com" in the above example. You could maintain your own dynamic DNS record, but you don't even have a static IP address. Chances are you're looking for less expense and hassle, not more. Fortunately, there are a number of providers out there willing to do the upkeep for you. Their fees range from free, to free with a one-time charge, to a monthly or yearly fee. Most charge more if you want your own domain name, such as yourdomain.com, as opposed to a subdomain like yourdomain.yourdnshost.com.
There are a lot of providers of dynamic DNS to choose among. Personally, I have had great luck with DNSMadeEasy.com, but others recommend different providers.
In addition to a provider, the other thing you need is a client. The client is a small piece of software that runs on your local hosting machine. It detects the machine's current IP address and, when that changes, sends a notification to the DNS provider. Detecting the IP address is a simple matter if your computer is connected directly to the broadband line, but if you have a router or NAT in your setup, and several computers sharing your connection, then the process becomes a little sniffier, and the client has to be clever enough to get the IP address that the router or NAT machine is using.
A few different attempts to standardize the process have been made. This means that you have to get a client that's compatible with your particular provider, and, when you change providers, you may have to change clients as well. I have argued before in these pages for standardization of various things, and I still think it is a wonderful thing, despite the initial hassle. But, last time I checked, we still live in the real world. A given provider's site should tell you what clients you can run.