Wash and dry the zucchini. Trim off the stem and end.
Shredded Zucchini
Shred the zucchini using a box or hand grater.
Wrap it in a clean dish towel or cheesecloth. Wring out the water, repeating several times until the zucchini is mostly dry.
Transfer the shredded zucchini to a freezer-safe bag or container. Seal tightly. It can be helpful to freeze it in 1- or 2-cup portions, since those amounts are often used in baked good recipes. Store in the freezer for up to 3 months.
When you want to use it for baking, let it thaw in the fridge overnight. Drain any excess water before adding to recipes. However, if the recipe calls for zucchini that hasn't been drained, keep the water to use in the recipe.
Zucchini Noodles
Turn the zucchini into noodles using your preferred method.
Transfer to airtight freezer-bags. Seal tightly, removing as much air as possible. Freeze for up to 3 months.
Add noodles straight from frozen to soups, stir fries, or other hot dishes without thawing first. They won't hold up well in cold dishes.
Zucchini slices
Slice the zucchini into rounds or half-moons.
Bring a pot of water to a boil. Drop the zucchini in the boiling water and cook for just 1 to 2 minutes.
Immediately drain the zucchini, or alternatively, use a slotted spoon to quickly remove them from the pot. Transfer to a bowl of ice water. Let them sit for a couple of minutes.
Drain the slices, then pat them dry. You want to remove as much water as possible.
Spread the slices out on a baking sheet. Put it in the freezer, somewhere it won't get bumped, for a couple of hours until the zucchini is frozen solid.
Transfer the frozen pieces to a freezer-safe bag or container. Seal tightly. Store in the freezer for up to 3 months.
Add frozen slices directly to soups, stir fries, and other cooked dishes without thawing first. They won't hold up well in cold dishes.
Notes
Keep in mind that zucchini has a high water content, so frozen zucchini does tend to get softer and mushier than fresh zucchini in recipes. If you really need to preserve the texture of zucchini for a recipe, use fresh instead of frozen.