Here is how I used to make it using a vegetable peeler and leaving the bitter skin on the zucchini.
Here is how I make it these days - angel hair-style without the skin - fabulous!
Here is a video by a raw food enthusiast. It's amusing to me to see the fancy stove and oven behind her. Looks like she has an amazing kitchen - phew, beautiful! Anyway, ignore the fact that she likes to eat it raw, the video will show you exactly how to make zucchini pasta. Find the video here.
Here is a nice-looking SPIRALIZER - click to see.
Here is a GREAT TUTORIAL of how to cook your zucchini noodles....scroll right down until you find the cooking methods! (CLICK THE HIGHLIGHTED TEXT)