The easiest way to grate zucchini is with a food processor and a shredding disc.   You could also grate the zucchini using a box grater.  Whichever method you choose, be sure to squeeze out as much of the liquid as possible before adding it to the muffins. You can do this by wrapping the zucchini shreds in a clean dish towel or several layers of paper towels and wringing it out over the sink.