Anyone know how to make changes to a DNS server?

Reason I ask: I own a domain (who doesn't ), that is being hosted by a company. Since right now I'm only using it for the email and as a quasi storeage space I would really like to move it to my computer (I have all the software to run email and web server). The problem is that I'm on a Dynamic IP for my DSL and for some reason I have to power cycle my modem and router at least once a week (thus getting a new IP). I would really like to be able to make my own changes instead of having to pay someone to do it for me.

I have checked into the services that will do it for you but all I have found require that you subdomain or pay them. And besides I really like knowing how to do stuff myself.