Use a dyndns like service, for aliasing a dynamic ip adress, and on your registrar's control panel search in the DNS managment or "forwarding a domain name" to redirect it, to the dyndns domain.

This is not the best solution to have a website.

Yes setting up dyndns is a good solution.
Even better, you can use www.no-ip.com.
This comes with an 'auto update tool'
Which will update your IP to the domain name you've bought.

Thus, you can
1) have your server running from home.
2) have your domain point to your no-ip.com address which will point to the IP of your machine.
3) you have an auto update tool to update your no-ip.com address when your IP changes.

erm, i may be completely wrong here, but don't you register your IP address with the people you bought the domain name from for it to be included in the upstream DNS?? i'm sure google etc do not use dyndns/no-ip