There are quite a load of opinions here. Some people will tell you that scrubbing is the best, others will say that rubbing/isopropyl alcohol makes the contacts rust.
I tend to VERY gently rub a pencil eraser on the contacts, as it removes the oxidized layer on the contacts. I then clean them using alcohol and a Q-tip. And for the eraser part, do it only if you have the special nintendo security screwdrivers to unscrew the cartridge, otherwise it is too much of a pain. And if you can unscrew it, alcohol is fine :). Get some 70% or 90% alcohol, or even some 50%. The most concentrated you can find, really.
For female cartridge connectors (the connectors inside the consoles), I usually take an old plastic gift card and I wrap up a piece of fabric around it (make sure the fabric that you choose won't leave any kind of string coming off of it into the connector). Then, I dip it into alcohol and I put it into the console connectors in an in-and-out movement. Be sure not to go diagonally, otherwise you may bend the pins.
As I said at the start, there aren't really any kind of "universal method". Try different methods and think with your head. For instance, never scrub the contacts with anything harsher than an eraser. And even then, I wouldn't use the eraser too often because if there are little dust particles on the eraser you will be scratching you contacts. A couple times is fine, but be reasonnable :).
Have a nice day into the wonderful world of retro gaming !
EDIT: Oh, yeah, and by reading other answers, research the products you are using. I wouldn't use a brass polish, but I haven't researched it. Really research stuff before you use them. And, for the love of god, please, don't you ever, EVER use sprays. They are imprecise and they could cause shorts. Dip your Q-tips into the alcohol or something.