First you cut the fabric off the frame. I used a seam ripper because you can stick it in the little loops of thread and cut them without touching the fabric.
Before going any further, I reinforced the seams from the outer edge in to the last snipped attachment point. The sewing unravels very quickly, but I realized I might need to open up the seams to make the bottom work. It ended up being a convenient place marker later on.
I decided to use half of the sections to make inner pockets. For this umbrella, that meant 2 inner pockets. If your umbrella has only 6 sections, you'd could leave 4 sections for the outside and get one pocket or have just one flappy pocket and 2 inner pockets. I wanted to keep the closing tab to be able to pack the bag up, so I made sure to leave that section as an "outer" piece. I folded the fabric in half along seam lines and just sewed the two outermost quadrants together along the seam line, down to the same point I stopped reinforcing.
Then I lined up the outermost corners with the opposite new seams and sewed along that line to the same point. If you look at the open end of the 8-panel bag, you can make a square with the four outer panels and a four-layer diagonal. 3 pockets for the price of 2!
Next, I turned the bag inside out at the center of the pocket diagonal and basted that shut. I noticed that the bottom corners I had just sewn weren't anywhere near each other, so I took out the center of the seam, pulled them into place and sewed it again.
You can still fold it up and throw it in your bag like the compact umbrella it once was, only now your wallet won't get wet. I'm not sure how practical it is for carrying large amounts of stuff, but it was fun to figure out how to make it and I like the way it looks.