You need to shut the water off to the faucet before you take the cartridges out. Otherwise there'll be water blasting out of the hole the cartridge screws in to.
You need to find the valves that shut the water off to the faucet.
Then, probably the best thing to do if you have very limited plumbing experience would be to just replace the whole cartridge rather than repair the cartridge.
You should be able to find the name of the manufacturer of the faucet somewhere on the faucet. Then, go to any hardware store and they will sell new cartridges for most faucet manufacturers. If the faucets are really old and you can't buy replacement cartridges for them in your local hardware store, you can always order parts for old and obsolete faucets from any hardware store that buys from Kissler & Company. Kissler will tell you who in your area order from them often. Kissler has a $200 minimum order, so you won't be buying from them directly. You need to find the place closest to you that deals with them a lot so that you don't have to wait a long time for the store to accumulate $200 worth of merchandise to order from Kissler.
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Your very best bet, if you have access to a digital camera, is to take a picture of what you're looking at, and post them in here, and people can tell you step-by-step what to do to fix the leak. Also, what you need to do to fix a leaking faucet depends on where the faucet is leaking from. And, even thought there's a lot of similarity between cartridges from different faucet manufacturers, there are enough differences that it's not possible to give you a step-by-step procedure to follow that will apply to every faucet.
We could help so much more if we could see what you're seeing.
So, first step is to find the manufacturer's name somewhere on the faucet. Next step is to beg, borrow or steal a digital camera. Then, register at a web site like photobucket or imageshack where you can upload your photos and link to them.