Place your garden shovel on the ground between the light that still illuminates and the one that is not working. The cut wire is between these two lights.
Turn off the transformer to the landscape lighting. Some transformers require you to unplug the unit, while others have a power switch to turn to the "Off" position.
Starting at the light that was not illuminating, begin digging up the wire with the garden shovel. Dig slowly and carefully around the wire so you do not puncture it in another location. The wire is only a few inches under the soil. Dig the complete wire from the ground.
Cut the damaged area of the wire out with a pair of wire cutters. Remove ½ inch of the wire insulation from the two ends of the cut wire with wire strippers.
Pull open the cap on the waterproof wire nut. Twist the ends of the wire together and insert the end through the cap of the wire nut. The cap has a small hole with perforations that you push the wire through.
Insert the ends of the wire through the sealant and twist the wire nut clockwise to secure both wires. Close the cap and push it until it locks.
Place the wire back into the ground and cover it up with the soil. Turn the transformer back to the "On" position or plug the power cord back into the outlet.