Most kitchen faucets use a simple cartridge inside. Usually a couple of o-rings hold it in place. pretty simple job. If its a single handle, there should be a screw under a small cap near the base of the handle, then the top of the faucet just threads off and there's the cartridge. If its brass, replace the whole thing, if its ceramic, you can just replace the o-rings. a double handle is basically a threaded valve, under the handle, the base should unscrew, then 'turn the faucet on' until the handle comes out. should be a tapered gasket in there.
(do i need to mention to turn the water supply off before attempting these repairs?)