Buy a new cord at a hardware or gardening supply store. The package should indicate the length of the cord. You also can contact the umbrellas' manufacturer to buy a cord made specifically for the umbrella.
Inspect your umbrella to see where the cord broke. Often, the cord is breaks at the winding bolt. If that is the case, don't open the umbrella.
Look at how your winding bolt is held together. Remove the retaining rings by sliding a putty knife underneath the rings. Retaining rings are the hardware attached to the winding mechanism.
Remove the nut on the other side of the retaining rings. Take off the handle. Tie the new cord onto the broken end of the cord. Stick a grabber tool in the crank bolt hole to latch onto the broken end of the cord in the umbrella. Cut the end that is attached to the umbrella end. Pull the new cord all the way through with the top pulley.
Stick the grabber tool in the crank bolt to pull out eight inches of the new cord. Burn, with a lighter, the end of the cord to prevent it from unraveling. Make a knot. Place the knot back through the crank bolt and reassemble the winding mechanism.