How do you repair a faucet stem leak?

With the faucet shut off, take the handle off and under it is a nut around the stem. There is either an O ring under the nut, a fiber washer or stem packing depending on what type of faucet it is. Replace which ever it has and that should fix it. If your faucet is a screw type, the handle turns several time when opening it, you can probably take the nut off, wrap two or three wraps of stem packing around the stem, clockwise looking down on it and replace the nut and tighten. This will compress the packing around the stem without replacing the cone washer in the nut or all of the old packing.