Oh right, it had a gaping hole in the top layer. Except really it didn't. What happened was that the fabric had ripped away from the ribs in two spots, creating a flap. Not very waterproof, but super duper fixable.
All I needed was a needle, thread, scissors, and a scrap of fabric. I used an old t-shirt, but you could use an old sock, dish rag, or piece of ribbon if you care about it looking nice (1/2 inch or wider should be fine). I tend to not care about the appearance of my umbrella repairs, because when its rainy I just want the umbrella to work, not win a fashion award.
How to repair this umbrella in about 7 minutes.
Step 1: thread the needle so that the thread is doubled for the entire length (umbrellas get beat up, so you could use 4 strands of thread).
Step 2: Attach the end of the thread through the hole at the end of the umbrella rib and tie a knot (photo below). This will anchor whatever you sew to the frame of the umbrella and help it from sliding around too much.
Step 3: Fold your scrap fabric in half so that it goes over the end of the rib point, secure with a few stitches.
Step 4: Pull the umbrella fabric down towards the end of the rib and sew the scrap fabric to the original umbrella fabric. I tend to leave a little slack so I don't pull the umbrella fabric taut, I don't want to put strain on another part of that layer and cause thread to break somewhere else.
Step 5: Repeat steps 4 & 5 for as many ribs as needed.
Step 6: Sit back and enjoy your newly mended umbrella (sporting a repair that sort of looks like fangs!).
Alternate fix: if you only have a needle and thread, but no scrap fabric, you can make very long stitches and secure the original umbrella fabric to the end of the rib through the small hole. It would be hard to pull the fabric as tight as it was originally, but it would still be a serviceable umbrella.
Don't throw out those good umbrellas, repair and reuse.
Happy freestyling!