I believe the proper name for the common pigeon is "rock dove." At least so says one of my bird ID
books. A little easier to swallow, that way.
As for squab, you'd need some sort of housing (dovecote), of course. Could probably be as simple or complex as you wanted. I'm pretty sure you need at least two (sets of?) nesting boxes per breeding pair, as they'll begin laying eggs before the previous batch is ready to harvest.
I'd think luring in these "rock doves" would be the most difficult part. Once they're in, keeping them confined for a bit (a week? two?) and hand-feeding them
should keep them coming back once you let them loose.
Perhaps a hybrid approach would be your best bet. Purchase domesticated doves, acclimate them to your dovecote, then let them roam the city for food. Free meat.