There are two things to remember when it comes to knowing how to harvest zucchini: pick them young, and pick them often. If you do those two things, you'll avoid being stuck with overly large, tasteless (and sometimes bitter) squashes. You can harvest zucchini at any time. Baby zucchini (two to three inches long) are popular in some restaurants and farmer's markets due to their mild, sweet flavor and attractive appearance. Generally, you'll want to harvest regular zucchini when they're about six to seven inches long, and round zucchini when they're about the size of a pool cue ball (there's a reason one of the most popular round zucchinis is called "Eight Ball" after all!)
To harvest, you can snip the fruit from the plant with pruners or scissors, or just give the zucchini a bit of a twist -- the stem should come away from the rest of the plant easily.