How do you start a community garden?

Call the town government or the city council or your alderman or your selectman.

Here’s a fact sheet that gives you all the details

First, you find a community with which to commune. You could do this by posting signs with tear off strips for your phone number. (super markets are good. so are churches) The sign should announce your purpose. When people call, take their name and number and make a list of them. There’s your community. Then have a meeting and discuss the fact sheet that @gailcalled gives above. It may be too late for this year, but perhaps you could start after you get settled into your new place.
You could always dig up your front yard and have a veggie garden. The people who live around you would be happy to share the results, I’m sure.

I just made some tear off sheets, thanks for the advice!
—Change of plans with the moving, it will happen a little later so now hopefully I have enough time