Not being a hunter, I need instructions on how to "field strip" them; we have zillions of them here in the desert, and whenever I hear a thump in our back glass, I'm likely to find another that's flown into the window and snapped it's little neck.
You have an interesting situation - sort of like getting manna from heaven!
Here's my suggestion. Almost all the usable meat on a dove is in the breast. You can pick the feathers off and gut the whole bird just like a chicken, but it's extremely time consuming and the amount of extra meat you'd get is negligible. Just insert your fingertip under the breastbone where it covers the abdomen and pop or rip the whole breast off the carcass. You can then easily clean the remaining skin and feathers off the breast.
Since you're only getting a bird every now and then, simply save each cleaned dove breast in a ziplock freezer bag until you have enough for a meal. When you have a sufficient number, thaw and marinate them for about an hour in your favorite marinade (zesty italian dressing is very good), then wrap each breast with a strip of bacon, place on skewers and grill quickly over medium-hot charcoal. Yum! Endless variations of this recipe are possible limited only by your imagination.