You can use one of free dns services. I recommend everydns.net
(I'm using it for some of my domains, including phpbbstyles.com instead of hoster's dns, so if there are problems with this server users can always resolve domain's ip. helps a lot when server is slow).
When registering domain (or later when editing domain data) set nameservers to ns1.everydns.net and ns2.everydns.net, then register on everydns.net, add new domain to your setup and create A record for yourdomain.com and www.yourdomain.com
with your home computer's IP.
If your IP is dynamic then get some dynamic dns like no-ip.com and in everydns.com setup CNAME instead of A record pointing to yourdomain.no-ip.com instead of your IP.
Do NOT pm me, I don't visit this forum anymore, don't own it, don't provide any support and don't moderate.