The metal structure of your umbrella should have a plastic or metal tip with a hole through it, which is where the umbrella is stitched to the structure. This hole will likely be fairly wide, so use the thickest, strongest thread that you have in your stash. The denim thread that you use to hem blue jeans invisibly works well, but so does thick embroidery thread, or even yarn.
Pass the thread through the eyelet, then through the hole in the umbrella’s tip, and tie it in a snug overhand knot. Don’t try to pull the two as tightly together as they are at the other, factory-assembled tips–the extra stress on a once-broken part is unnecessary, and a difference of a fraction of an inch in the symmetry of your umbrella’s tips certainly won’t be noticed.