this help article for instructions.
Note that you can't map to a "naked" domain, such as example.com, you have to map to a sub domain. like www.example.com. To make the naked domain work you have to forward it to the www sub domain.
The condensed version of the help article is:
If you have more than one Google Site you can map one of them to a different sub domain. As an example, in my domain, k8oms.net, www.k8oms.net is mapped to my main Google Site. I also have a different Google Site that is mapped to tour.k8oms.net.
Here is how I did it:
Some people want their site to have a "Splash Page" that has no header, sidebar, etc.
For an example go to splash.k8oms.net
Note: I use the 'splash' sub domain only for demo purposes. Normally you would follow the instructions above.
If you do not use a domain please see these instructions by PhilRidout
In addition, if your domain registrar allows it you can forward sub-domains anywhere. GoDaddy allows for 252 forwards.
Be sure to forward your naked domain 'yourdomain.com' to 'www.yourdomain.com'.