Prepare Zucchini Pasta Sheets: Carefully slice zucchini lengthwise into very thin ribbons (about 1/16-inch thick) using a mandoline slicer if you have one, or a very sharp knife. Lay the ribbons on clean kitchen towels in a single layer. Sprinkle them lightly with salt and let them sit for 30-45 minutes to draw out extra water. After resting, gently pat them very dry with more clean kitchen towels.