How to repair this leaking garden faucet - update (broken stem)
Good start the nut is the valve packing for the shaft if it is leaking there you need some valve stem packing. This is usually expanded PFTE sometimes with graphite embedded. Several wraps 1/2 dozen then put the packing nut back on tight and this will stop valve stem leaks. If the leak is out the faucet unscrew the handle and there is normally a rubber washer held in place with a screw. The new washer will look like a volcano a cone with a hole. These get squished over time and look flat but a new one is usually volcano shaped wide side should fit tight on the shaft and the screw holds it in place. Put it back in at this point I usually add some valve packing around the shaft and tighten the nut, with a new washer you may have to tighten it a little to get the stem packing tight. But that’s the complete rebuild. I would invest in a kit of different sized washers my box is ancient and I buy more washers, packing and orings as I use them up a inexpensive kit of parts for a home owner.