Best way to fix a corroded shut-off valve under the sink

Don't waste time trying to clean or lubricate a corroded valve - you'll just delay the inevitable leak. The previous answers aren't wrong about replacement being the standard move, but there's a middle ground worth considering first. If the corrosion is only surface-level (white or light green crusty buildup) and the valve still shuts off cleanly with no drips, you might buy yourself time with a wire brush, some white vinegar, and a protective coat of spray lacquer designed for metal. This works best on brass valves. That said, if the valve is already weeping or won't turn smoothly, skip the DIY cleanup entirely.

For actual replacement, the job is straightforward. Shut off main water, open a faucet downstream to relieve pressure, place a bucket under the valve, and unscrew the compression fitting connecting the supply line. The valve itself usually screws or compresses onto the copper stub coming from the wall. A new quarter-turn ball valve (much better than the old gate valves) runs cheap and installs in minutes with an adjustable wrench. If you're uncomfortable working with water lines or the fitting is badly corroded and stuck, calling a plumber makes sense - sometimes the stub itself is compromised and needs professional soldering to replace.