Some of your have probably noticed that when your NAT is strict you can't join your friends with the same NAT. Well, there's two ways to fix it -- port forwarding and setting a DMZ. The latter is the easiest so I'll post how to do that first.
Firstly what you need to do, is go here:
PortForward.com - Free Help Setting up Your Router or Firewall
And choose your router. On the page, look at the first couple of steps. It will tell you to enter an IP address into your browser (ie 192.168.1.1) and then enter the username and password. Do that until you get to your router settings. Stop following that guide afterwards, because it's for port forwarding and not DMZ'ing.
Once you're in the router settings you need to find the "DMZ" page. Have a look through the menus -- it's probably under "Security", "NAT", "Gaming and Applications" or something like that.
You will know you've found it when you simply see a box to enter in an IP, and sometimes a check box saying "Enable". When you find the box, enter 192.168.1.50 into it. That's it, just save if you can.
Easy eh? Not finished just yet though. Now you need to go to your Xbox. Go to the last blade, the settings one, and choose Network Settings. From here choose Edit Settings and choose IP Address. Set it to manual and use these settings:
IP Address: 192.168.1.50
Subnet Mask: 255.255.255.0
Default Gateway: Use the IP address that you typed into your browser to get your router settings up. Normally 192.168.1.1.
Now try to connect. Your NAT should be open. If it isn't, restart both your router and Xbox 360.
I typed this really quickly, so if it's confusing in any parts just let me know. I can post how to port forward too if anyone wants, but DMZ'ing is far more effective and easier.
If your DNS fails then do this:
Go to Start > Run and type "cmd". Then type "ipconfig /all". Take a note of your Primary DNS in there.
Then go to your Xbox, settings, network settings, edit settings, DNS Server, manual and use:
Primary DNS: whatever you took note of from ipconfig /all
Secondary DNS: not needed.