Step one is getting to know your umbrella. Each umbrella will have some clips or strings holding the fabric to the frame of the umbrella, some sort of tips for each wire that attaches to the fabric as well and a cap on the top of the umbrella that will need to be noted and carefully removed.

On this particular umbrella (and I assume most from looking at their construction) the cap is pressure fit onto the top. This I found easy to remove with a set of pliers and a few good taps from a hammer on the pliers once I was clamped down. Alternately if you feel comfortable with a dremal tool you can carefully cut it off as well.
Here we have an example of some of those strings tying the fabric to the frame. For our disassembly we are doing 2 things with these, marking them so we can retie them with the new material and cutting them for disassembly.
Here we have the tip caps on our umbrella. Most umbrellas have plastic tips now that make our job here easy. To remove the tip we simply pull it off the wire end. Then using your razor we will cut the string securing the tip to the fabric. As there is one in each corner marking them is not necessary.
Here we have the bare skeleton of the umbrella fully exposed. You can see that the main support wires the material attaches to is about the same length as the umbrella.
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