Cleaning the NES Game System
I am not responsible for any damage that may happen by following these instructions.

Step 1
The first thing you need is a Philips screw driver to undo all the screws, an eraser (it's better to use one on the end of a pencil) or toothbrush (preferably not yours) some electronic cleaning solvent (Windex, or a 50/50 mixture of Rubbing Alcohol and water work fine as well) and a whole mess of  Q-Tips remember to unplug the NES and turn it on to remove any electricity.

Step 2
Now you need to turn it over and undo the six Philip's screws, then holding it together turn it back over and take the top off this will leave you with a big silver cover show in the picture below.
(The Numbers are where the screws are)

Step 3
To take the silver protective cover off there a seven screws holding this down.
(The Numbers are where the screws are)

Step 4
Now unscrew the games slot and the RF/AV and Power box.
(The Numbers are where the screws are)

Step 5
Now lift the main board out and pull out the two controller leads and and Power/Reset Button lead and turn the board over.

Step 6
The three leads have been removed and the board has been taken out, yet another silver cover to be removed.

Step 7
Now to pull the black connector off of the main board and you will see the silver pins which it attaches to.

Step 8
Now use the eraser (or toothbrush) on the silver pins where the 72 pin connector was and get it as clean as possible. Now get a Q Tip and spray each end with some electronic cleaning solvent and again rub it on the silver pins where the connector was. If done right will make it like new, now take a dry Q Tip and rub any solvent left on the pins off. If you have done all this and it still didn't help you will need to buy a new 72 pin connector either from eBay (give or take $10) or MCM Electronics ($7.99) (USA Only)
If you're exceptionally careful, you can clean the 72 pin connector with the solution and a pair of fine tweezers or paperclip with something to scrub them at the end.

Step 9
The NES is now all put back together and like new except the the 72 pin connector (unless you replaced it) this can easily be cleaned if you have a "Cleaning Kit" by Nintendo which can still be bought from there web site. www.nintendo.com. If you don't feel like it, however, you can try either the way suggested above, or cut a piece of folded over cardstock  to the proper size, put the cleaning solution on the end by the fold, and insert and remove the cardstock from the 72 pin connector inside. This isn't a very good method, however, and I suggest either buying a replacement 72 Pin connector or using the NES Cleaning kit.

Cleaning NES Game Cartridges
I am not responsible for any damage that may happen by following these instructions.

There are lots of ways of cleaning the games most of the time I just spray them with your cleaning solution and use Q Tips to rub the connectors (if you have the cleaning kit use the thing that comes with it for cleaning the games it works much better) but some times you will get one which no matter how many times you clean it will still not work first time or will not work at all. In this case you will need a 3.8 mm Security Screw Bit, an eraser (same again better if it's on the end of a pencil) some cleaning solvent and 4 or 5 Q Tips.

Step 1
Take you not working game pak and 3.8 mm security screw bit. Available at MCM Electronics. I Recommend buying a whole set, 'cause you'll never know when you'll need them next, and it's best to be prepared.

Step 2
Undo the three screws in the back (you don't need a 3.8 mm security screw if you have a REALLY old cart with five screws because there not security screws.) IF You happen to be opening up a Tengen game, they happen to use Torx Screws. I'm not sure of the size right now, but you should already have a set, since you're all about electronics, right?

Step 3
Open it up and take out the board (PCB). Realize that what you spent all your allowance on is a tiny little board, and a MUCH BIGGER plastic casing. Feel Gypped and Cry. (If you've ever seen a Famicom (Japanese NES) cartage, then you'll know why the board is so small.

Step 4
Use an eraser (or toothbrush) to clean the pins and then spray with a cleaning solvent and rub with some Q Tips each side, then use a dry Q Tip to get the solvent off.