How can I share the Internet over an Ad-Hoc network?

You should be aware that the ad-hoc part of the 802.11 standard (wireless) is very poorly implemented by some wireless network device manufactures. Thus it is not uncommon at all to encounter two laptops which are simple incapable of communication with each other over an ad-hoc network.

I work with ad-hoc networks almost daily, I'm studying networks and distributed systems. And from experience with many poor ad-hoc implementations, we always make a point of using the same 802.11 hardware for all units we want to communicate in an ad-hoc network.

I have done this the other way around, by connecting an ethernet cable to my Xbox and sharing my Wireless internet connection. You should be able to do it the other way around.

You should open your Local Area Connection properly and check the "Share this connection" option. That will turn your wireless connection into a DHCP server that will other computers to connect and get an IP address. Your computer will act as a NAT and route traffic through the Ethernet.