First of all you need to be running your chosen webserver on your laptop whether or not its Linux Windows or anythign else. Then like joxley1990 said you need a DNS server running as well.
If your not using Linux I strongly recommend it if you're trying to run a webserver from home. IIS is easier to use but lacks the serious configuration options that Linux has but if youre looking for a quick solution then IIS is probably for you and the new version in Vista is much better than the old ones.
Unless you know about *server security* it's just a matter of time before you're webserver and your notebook gets owned. Reason I say that, people know you're running a webserver from your personal box yes you will be more vulnerable to attack.
If you know nothing about "server security," I wouldnt recommend doing this, espically on my *personal* notebook thats for sure.