I would like to have my domain pointing to a computer I have at home
Its depends on what you mean by that statement.
If you want the IP address of "mydomain.com" (replace with your domain) pointing to your home machine, all you need to do is add a hostname entry to your existing name server that is hosting your domain (is the authorative name server) and add the entry for "mydomain.com" (or whatever).
However, if you want control of the domain to be pointed to a server at home, then you have to call up the domain registry from which you leased your domain from and have them point it to the IP address of the machine you have running at home with the name server software.
An an example:
Anandtech's domain level address for
anandtech.com is 168.143.107.162
Anandtech's authorative nameserver for
anandtech.com is 168.143.107.2 (aka, e11-1.sgdc.eicomm.net)
EI Comm handles Anandtech's naming services. Yet anandtech.com points to a server that Anandtech operates. You don't need both. However, its easy to do if you want.
There are limitations...
The authorative nameserver must have a static IP. No DHCP!
If your home computer uses DHCP and you want it to handle your domain level hostname, you're domain's DNS server
MUST accept dynamic-DNS updates (DDNS).
If you want to take control of your domain's nameserver authority, you must contact the company that you registered the domain with. If you purchased it through your ISP, you'll need to regain control of it from them