As far as killing pigeons go, once you find where they are roosting, usually in a grainary, show up there just at dusk, the pigeons will be roosted for the night so they are easier to sneak up on, and not in a big hurry to leave the roost, then you have to flush them out and shoot them. Again getting their at dusk can sometimes get you a second or third flush as they are reluctant to leave, and they may not all leave at once.
As far as cooking them, your on your own.