Pop the Faucet Cap
Your first step is to shut off both hot- and cold-water supply lines under the sink, and here Sorrell advises caution. Shutoff valves in older plumbing systems can be corroded, especially when connections are threaded instead of soldered. "I've had them crumble right in my hands," Sorrell says. An uncontrolled geyser under your sink is no way to get started, so if the shutoff is suspect, use the main shutoff valve, located where the waterline enters the house or at the pressure tank. Another preliminary step: Block off the sink drain with a rag so small parts don't disappear.
Pop to the cap on the top of the faucet with a screwdriver or utility knife, then remove the single screw to free the faucet lever. You might need to work the lever back and forth gently to pull it up.