You pick them out of the meat when you start chewing it. ;o)
That's the least desirable method. Better is to check the bird over as you pluck it.
Shot choice has several variables that are all interconnected. The smaller the shot number, the larger the pellet. Large shot has a longer range (greater sectional density, even for a projectile as inefficient as a round pellet), but fewer pellets per shell. Small shot gives denser patterns at shorter ranges. The "choked" section of a shotgun barrel near the muzzle can also expand or contract the "shot string".
The type of game and the distance of the shot determine you ammo choices. Goose hunting requires heavy charges of large shot, which brings increased recoil. You're trying to bring down the avian equivalent of a B52, and you just hope one or two pellets connect with enough energy to bring it down.
Small birds that hold cover until the last second break out like rockets in all directions. You want a shell with a light load of small shot so you can get a cloud of shot out there quickly. Birds like quail and grouse are so fast you usually don't have time for a second shot before they are gone.
The odds are all stacked in favor of the bird. You need a good dog to alert you to a possible target in time to get yourself ready. Otherwise, you probably won't know there's a bird there until you almost step on it. It increases the excitement of the hunt, but not in a way most people would consider desirable.
I hear a dentist's drill ...!