How can I connect my Xbox 360 to Xbox Live through my Laptop?

What steps do I need to do in order to connect my Xbox to Xbox Live through my laptop? I can connect them physically, but I also have a wireless adapter (if it's possible to create a bridge using the adapter as well).

The problem is that I am in an hotel for the next two months, forced to live off their wi-fi. And although my laptop connects to it without a problem, my Xbox 360, even though it has a wireless adapter, does not. It also doesn't present a very helpful error messages, helping me locate the problem. So I'm thinking that connecting the Xbox through my laptop is probably my only hope.

Here's a link on Networking with the Xbox 360, from xbox.com.

Here are a couple of links from instructables.com that seem to cover exactly what you're trying to do.

And here's a video of the same thing.