We take birds for granted. Some are domestic and get eaten (or their eggs are eaten). Some are wild and are hunted for food. Some are wild, and we give them something to eat in bird feeders. We admire their flight and enjoy their songs. It's not often that we treat them as partners.
Medieval Europe had the same birds as modern Europe (though not in the same proportions), but they had more hunting hawks, trained to be partners in hunts, just as a modern pointer or retriever (dog) can be a partner to their master in the hunt. (Or not. The Labrador retrievers I've known would either not figure out where the duck went or would carry it off for their own purposes. Training is everything.)
Most farmyards had chickens, free range, that lived on spilled grain and insects. Keeping down the insects was an important function, nearly as important as laying eggs Eggs were an important source of protein in the medieval diet, and when a hen got too old to lay, she became dinner herself. Geese and to a lesser extent ducks provided eggs and feathers (and dinner). Geese also made excellent watchmen, raising a great honking if something untoward happened at night.
Medieval people also ate songbirds, ones we would consider too small to bother with (and you would not have caught a medieval peasant putting out their precious grain for the birds to eat). The easiest way to catch them was to spread lime on a branch, so that when the bird landed on it, their feet would become stuck. They did however appreciate songbirds for their songs as well as their bits of meat. The nightingale especially appears in many a song and story, enchanting the lovers. (The US doesn't have nightingales. Our loss. Nighthawks are not the same.)
Aristocrats, but not peasants, used hawks in hunting. Training a hawk was a long and complicated process. The thirteenth-century emperor Frederick II wrote a book on falconry that is still respected today (an image from it appears below). The chief goal is to make the bird, from a very young age, think of the human as the source of food. Every respectable castle or manor had a mews, where the hawks were trained and housed. One could find baby birds and raise them oneself or buy them. Trained falcons made good gifts.
In the mews, the hawk would be tied to its perch, usually hooded to keep it calm and in the dark. Merchants might sew a hawk's eyes shut while transporting them. Hawks have much better eyesight than humans and can adjust for closer or longer distance in a way that is the envy of everyone wearing bifocals. But if they can't see, they tend to sit quietly, even if not happy about it.
Hawks had leather straps, called jesses, attached to their legs, which could be held (or grabbed). Generally the jesses had a bell, to help one locate a hawk that had not come back when it was supposed to. The way it was supposed to work was to ride out hunting with a hooded hawk sitting on one's wrist (the hand and wrist in a heavy leather glove because the talons are sharp). Then one unhooded the hawk and freed the jesses to send it up after a bird one was trying to catch. Theoretically the hawk caught the bird and brought it back, getting a treat as a reward. There are enough descriptions of chasing the hawk by the sound of the bell, of whirling the lure that was supposed to attract it, and giving calls to which it had been trained, to indicate that coming back didn't always work out right. This was part of the fun of the chase.
Birds caught with hawks became dinner. Wild ducks were normally caught with hawks, not with archery (and of course double-barrel shotguns were centuries in the future). Different hawks were used for different prey. Sparrowhawks (kestrels) caught small birds, as the name implies, big goshawks could take a goose, and there were others in between. Different kinds of hawks were considered more or less noble and thus more or less suitable for those different social station. A good master of hawks was highly prized.