To repair a broken leg on a wooden picnic table, flip the table over with the table legs facing upward. Fit the pieces of the broken leg together, if possible, and replace the broken leg into its original corner or socket.
Wrap the broken leg with masking tape to hold the whole leg upright while you prepare the rest of the table. With a 1/8-inch bit in a power drill, drill two holes into the table leg at a 90-degree angle, using the tabletop as a level plane. Drill vertically into the point of the break on the piece closest to the table top and through to the other part of the leg. Insert nails in each hole until the tips extend past the other side. Remove the masking tape.
Squeeze wood glue slowly into the break all the way around the leg. Use your body weight to gently press the leg pieces together, spreading the glue through the entire break. Place a 1-foot piece of wax paper with the wax side against the table leg, wrapping it around the entire leg. Tape the wax paper with masking tape to cover the glue while it dries over the next 24 hours.
Remove the wax paper, and use wire cutters to cut off the nail ends from the surface of the leg. File down any excess metal with a metal file to make it smooth and flush to the leg. Use sand paper to smooth any wood splinters or protruding glue. Turn the table back over, and test the strength of the leg before using again.