OK, when your browser actually pulls up a site, it pulls up the actual IP address in numbers. A DNS service is just a table of what URL is associated with what IP number. It lets you just remember a name of a site instead of keeping up with IP addresses manually. Google's DNS service tends to be more up to date and faster than a lot of local ISPs. If you change the DNS lookup on your computer, it will only affect your computer. The Google DNS walkthrough is very easy to follow, you shouldn't mess it up. Just remember what settings are currently selected before you change it and it should be a piece of cake.
For example, fiestafan.com is
http://190.120.226.30/