You May Have a Loosened Packing Nut
This is very common. The packing nut may get damaged or worn out over time. It may just get loosened due to water pressure. All you need to do is tighten the packing nut. You can use pliers or a wrench. Tighten it well enough but don’t be too forceful with the pliers or wrench. You may damage the nut with the excessive pressure. Chances are this will solve the problem only if it is the packing nut that has a problem.
Look at the Valve
If you still have faucet leaking from the stem, then you must look at the valve. The valve stem varies from one model to another and also among brands or manufacturers. You may have to replace the packing nut or the valve, you may have to replace the handle or the whole faucet if it is heavily corroded, worn out and outright unusable.
Shut Off the Water Supply
Remove the handle of the faucet, unscrew the packing nut, get to the packing washer and check if it is in working condition. You may be unable to find out if it is damaged to an extent to cause the leak. You may be unsure if it is the washer that is causing the faucet leaking from the stem. You can take it to a hardware store to have it inspected.
You Can Get a New Valve Packing or Packing Washer.
Get an identical one and preferably of great quality. Install the new valve or washer, screw in the packing nut, get the handle back in place and turn on the water supply to check if there is a leak.
Get an Adjustable Wrench
All you would need to get the job done is an adjustable wrench, a 4-in-1 screwdriver, pacing washer, and packing string. If you are replacing the whole faucet, then, of course, you would need a new faucet.