Fixing a leaky faucet really isn't that challenging once you know what your doing. Usually if your faucet is leaking it is an O ring that has simply worn out. This instructable is for two handled faucet.
Step 1: Removing the Handle
Begin by turning off the water under your sink. There will be two hoses with shut off valves.
Next, unscrew the screws at the top the handles. Many sinks have small caps on the top of the knob hiding the screws. If this is the case, gently pry off the caps to expose the screws.
Pull off the knob.
Step 2: Replacing the Inner Handle
Now, unscrew the nut holding the newly exposed inner cartridge. Lift out the cartridge.
Now, you can either buy new rubber O rings, or replace the whole cartridge for about the same price. The metal cartridges are more durable.
Finally, complete these steps in reverse order to reassemble.