How do I change my DNS Ip so it matches my gateway?

If you go to ( Network and Sharing > Change Adapter Settings > Right-click Adapter > Properties > IPv4 > Properties ) there are the options for Obtain IP Automatically and Obtain DNS automatically. If both are checked, then during the connection process your computer will broadcast to a DHCP server looking for an address. Your router will then respond, providing you with your NAT'd IP address and it's own DNS server information.

If you have this checked already but for some reason it doesn't match what your router's DNS server is, you can always configure it manually, by copying down your router's DNS and typing it into the field on the IPv4 Properties dialog.

I would only recommend doing this for a desktop though. If it's a laptop that will be traveling and connecting to different access points, you may have problems with your ISP's DNS servers not recognizing your requests as you will have a different IP, likely from a different provider - I'm not sure if that would be an issue or not. If you are having DNS problems though, and your router doesn't want to provide you the info automatically, (and it's a laptop), you might want to consider using a public DNS server. Google's DNS servers ares 8.8.8.8 and 8.8.4.4, and OpenDNS's servers are 208.67.222.222 and 208.67.220.220. Either option will work regardless of where you're connecting from.