The first thing to do after washing and drying off the zucchini is to shred it. Cut off the ends and then use a box grater and with one hand hold onto the grater and the other hand on the squash.
You need to use some cheesecloth, paper towels, or coffee filters to squeeze the water out of the squash. Take a small amount of shredded zucchini at one time and place it in the cloth and squeeze.