Typically, people would wait for them to land.

Cheeky, perhaps, but that's how it was done. Modern shotgun hunting is a fairly lazy sport, done more for fun than for food. People march through a forest making all sorts of noise and startling birds into flight so the hunters can shoot them on reflex.

When it was an important part of your diet, what you would do is be very careful not to make any noise, try to cover up your scent, look for their shapes in the brush, and kill them with whichever missile you prefer.

Edit: Oh! I forgot to mention Egyptian fowling! Egyptian noblemen would have their servants cast nets at the fowl they hunted, and while the fowl were struggling to take off the hunters would kill them with spears and throwing clubs.

In Medieval times, in Europe and the Middle East, flying birds were hunted with hawks or falcons.

The art, or sport of falconry, was practiced by many of the upper classes, and, although birds could be flown at prey on the ground, they were often flown at gamebirds in the air.

Native Americans would shoot them with arrows, sometimes even attracting waterfowl with decoys. Some would also swim up to ducks and geese and catch them with their hands. http://www.doadecoys.com/history-of-waterfowl-hunting/