Best Storage:
Fridge
Keep dry (don't wash beforehand). Pop into a paper bag with one end open for air flow and into the fruit and veg crisper of your fridge.
Freezer?
Yes, however texture will change
To freeze, wash and slice zucchini into 1cm thick rounds. Blanch Lay out in single layer on baking paper on tray and Freeze overnight. Pack into containers for freezing. Grated raw zucchini can also be frozen - it will produce liquid when defrosted which can be drained.
Use it up!
Zucchini are high in water content so will be soft when defrosted. Use in baking and cooked recipes. eg. sauces, quiches, soups.
Need to use them up quickly? Instead of pasta, use zucchini to make zucchini noodles or Zoodles! Or grate and bake into quiches that can also be frozen for future meals.