When I clean my NES games I first open them with a 3.8mm screwbit. Then I take alcohol on a q-tip and clean both sides. Then I take a dry q-tip and dry the contacts.
Then I take a white rubber and rub both sides of the contact and take a q-tip to remove the rubber pieces that are stuck to the contacts.
Outside I use some wet paper to remove the loose dirt. For stickers I use glue remover (not sure what the english word is for this, but its some liquid fluid that you use to remove glue from bandage and stuff). I have never used this on the label, only on the cartridge itselv. Its pretty strong stuff so I'm afraid I would remove the label if I get this fluid on the the label. I also used some simular fluid once and then the cartridge started to melt. So be careful what you use.
You have been warned! hehe
Then the games are clean
This goes for SNES games too. You can open SNES game with a 3.8mm screwbit too. So its the same thing when it come to cleaning them my way atleast.