You can read about growing winter squash organically (or otherwise) all over the internet. I went to google.com and searched using these exact keywords:
growing winter squash organically and found hundreds of sites that told me how to grow winter squash.
Unfortunately I have been entirely spoiled by reading the excellent chapter on growing squash by Carol Deppe in her book
The Resilient Gardener. And I suggest you do too.
For Carol, squash is one of the 5 essential crops for being able to survive without recourse to grocery stores. (The others are potatoes, corn, beans, and ducks. Curious about why? I can't recommend this book too highly.)
Squash needs warm soil to grow. So depending on where you live, it might be necessary to get a start on the season by seeding them indoors.
Here where I live in the Pacific Northwest, the season is long enough between frosts. But we never get very warm, and squash like it warm. I need to start them indoors, plus warm up the soil with a plastic cover. (More on what kind of plastic cover another time.)
Here's the very specific issue we all face: The best-keeping squash are the giant ones, and the giant ones grow so vigorously that they outgrow their little indoor-seeding pots almost immediately. Their roots burrow through the bottom of peat pots and then are damaged when the seedlings are transplanted.
We can lose the whole crop this way, or we can end up with only the weakest, slowest-growing of the giant squashes: they're the only ones whose roots don't poke out of their little pots and hence get damaged during transplanting.
Carol Deppe, who is adept at
seed-saving as well as growing her own food, makes a strong case that this is the best way to lose the best characteristics of all giant squash.
Bush squash have a slower pattern of growth, and there's no problem with starting them indoors. The squash are much smaller and their roots aren't nearly as aggressive as those of their larger cousins.
So March is the time for starting squash. Start them outdoors if you're in one of the minority of places in North America where the soil is warm. And start bush squash (usually C. pepo varieties) indoors for transplanting. For the biggest (C. maxima) squash, you'll have to wait to direct-sow them directly in the garden when the soil is warmed up.
And that will give you time to read Carol's great book!