Placing a Zucchini in the crafting grid gives you a Zucchini Seed.
To farm the Zucchini, you plant and grow the seeds (or the Zucchini itself) on tilled soil, once they're fully grown you can right-click them, harvest the Zucchini and let them grow again. When harvested by right-click, the plant doesn't break, and yields 1-3 Zucchini.
Shapeless Crafting Edit
Here is a list of all recipes that use Zucchini: