I have borrowed this technique from this post, but made it shorter.
First, go into terminal and type this:
sudo gedit /etc/rc.local
ifconfig eth0 up
ifconfig eth0 192.168.2.1
echo "1" > /proc/sys/net/ipv4/ip_forward
iptables -t nat -A POSTROUTING -o ethX -s 192.168.2.1/24 -j MASQUERADE
Hookup your Xbox360 and your computer via Ethernet and boot up the Xbox360 without a game in it. Go to Network Settings and Edit Settings. Now change these things:
IP Address: 192.168.2.2
Subnet mask: 255.255.255.0
It will ask you to test these settings. Test Xbox Live. You should get an IP, but no DNS. Go to Edit settings once it's finished.
Your DNS should be the router's IP Address. To check it, return to your computer, right-click the wireless bars/two computers in the taskbar. Click 'Connection Information'. The Default route should be the router's IP address.