Open the video game cartridge up, you will need to get your self a game bit which you can find cheaply around the web, this works for most Nintendo Cartridge Games from: NES, SNES, N64 among others
You can use a 3.8mm Game Bit for Nintendo Cartridges.
Sega Genesis Cartridges would require a 4.5mm game bit.
Simply open the game using the bit on the screws on the cartridge. Some Nintendo NES Cartridges would require a small flat head screw driver.
Once the cartridge is opened take an eraser, and gently rub back and forth on the gold contacts on the game cartridge board. Make sure to rub the top and bottom contacts. Then proceed to polish the contacts with your shirt or a polishing cloth. Then reassemble.
Using Sand Paper:
Get your self some fine grit sandpaper, I generally would recommend 220 grit. Cut your self a small square and rub the sandpaper back and forth on the gold contacts of the game cartridge.
Blow in the Cartridge to remove and dust and debris.
Then take a cotton swab and dip in some standard rubbing alcohol, and rub the cotton swab back and forth on the contacts you just cleaned with the sandpaper.
This method words great with just about any video game cartridge.
For HuCards, just use an eraser on the gold contacts and rub back and forth, and then polish with your shirt or polishing cloth.
Cleaning Cartridge Based Game Consoles:
I prefer to use the sandpaper trick here once again.
Cut yourself a piece of 220 grit sand paper, and rub the sandpaper back and forth inside the cartridge slot of the game console.
Then blow to remove and dust or debris from inside the cartridge slot.
This works great with pretty much all cartridge based consoles from: Atari, ColecoVision, Sega, and Nintendo Consoles and many others.