Remove the canopy from your umbrella by first removing the ferrule (cap) and then carefully detaching the fabric from the spokes by cutting off the attaching threads.
Cut out a panel of waterproof fabric big enough to cover the torn section, and sew it onto the canopy with nylon thread. If a large segment of canopy is torn, trace the entire canopy onto the waterproof fabric, and cut out a new canopy. If your canopy is made of plastic, use an inner tube repair kit to make the repair.
Replace the repaired or new canopy onto your umbrella. Inspect the end of each umbrella spoke to find a small hole, and attach your fabric to these holes using a needle and nylon thread.
Inspect your stem to see whether it is wooden or metal.
Solder or weld a metal stem together at the point of damage.
Wrap a wooden stem in duct tape, or use wood glue to glue the broken parts together, and wrap the repaired section with wire or fabric. (See Reference 1)
Remove the broken spoke(s) from the umbrella.
Measure a section of wire to the same length as the original spoke, and cut it using wire cutters.
Using fabric and thread, attach the piece of wire to the umbrella stem and canopy while it is open.