cheapest way to fix leaky faucet?

Replace the worn part yourself, it's usually a washer, O-ring or cartridge. Shut the two valves under the sink, plug the drain so nothing small disappears, pull the handle off and take the old part to the hardware store so you get an exact match. Two handles and a squeak when you turn it off is normally a compression faucet and a washer costs pennies. Single lever is usually a cartridge, pricier but still way cheaper than a plumber.