I just cut up the zucchini into chunks, roughly 1 inch or so, and then I pressure can them in water and a bit of salt. I think the salt is like 1 teaspoon per quart. I use quart jars for the zucchini because I like using it as a filler in the stew. It takes on the flavors of the rest of the stuff in the stew.
I've also canned some quarts with half zucchini and half tomatoes, that also has to be pressure canned, not enough acid content for water bath canning. That also works out really well, but the zucchini shrinks a bit when you can it so the jars come out of the canner looking like you didn't fill them quite enough.
Almost forgot, I always peel the zucchini before I cut it up. The big ones have tough skin that's not really edible , and I don't care for the skin on the smaller ones. Just my preference.