I'm in the process of writing a book and part of the plot is a famine caused by a massive loss of farms in a society roughly equivalent to Europe in the middle ages. They don't poses gunpowder or firearms and they're in the process of over hunting the game around a major city, which forces them to hunt smaller and smaller animals like songbirds, water fowl, and eventually pests like rats.
Before I go inventing something stupid, I'd like to check with you all to see if there are any historical examples from around this time period of effective larger scale hunting methods for small game. I'm aware of snares and traps, but they seem like they would be mostly a secondary method to feeding a large starving population*. The setting is a mountainous heavily forested area if it's relevant.
Sorry if this isn't an appropriate question for this subreddit. If you could direct me to another place that's more appropriate, I would appreciate it.
Ducks were rarely hunted in Europe. They were domesticated like other animals, and were raised on farms alongside geese. Hunting was far more the sport of the rich than a means of sustaining most families. That being said, it is perfectly possible to shoot ducks with a bow and arrow. Using reeds as cover, similar to a modern hunting blind, has been seen in murals painted on Egyptian tombs, so it was likely a popular tactic.
The rich would have had a better time. The nobility almost exclusive raised domestic pigeons for their meat, giving them a better farmed food source than the peasantry. They also had the resources to engage in falconry to capture smaller wild birds.
Along the west coast of North America, during prehistoric times, ducks were netted using nets strung on poles in the lowlands near wetlands. They are described in the records of Vancouver's voyages in Puget Sound here. Other strategies included using decoys and shooting them with a bow and arrow. This is capabably demonstrated by the quality of canvasback duck decoys recovered from a number of Great Basin sites.
As you're not asking directly about Europe, I'll answer for New Zealand. Unlike most birds that replace their feathers in pairs, ducks moult all their flight feathers at once. The primary hunting method for Māori then was to catch them by hand from canoes during the moult, sometimes with the help of dogs. Ducks were also caught at night with snares. A string was stretched across a stream, and then nooses were hung from it at the correct hight to get ducks.
Source, from 'Forest Lore of the Maori' by Elsdon Best. The entire book might be relevant to you, as farming was often not particularly productive in New Zealand (the Māori were from Polynesia, so had brought tropical crops that didn't do very well in New Zealand, and wouldn't grow at all in the far south), particularly in the mountainous and heavily forested Uruweras where Best got most of his information from, so birds and fish were relied on in a way that most agricultural societies don't. The only other thing I would add from a different source is that in the South Island an extendable bird spear was sometimes used. The barb would be on the end of a relatively normal (if short) bird spear of ten or twelve feet long, sharpened at the butt, and then sections of a wood with pith would be used for the extensions. The pith would be removed a certain length down from one end, and then sharpened at the other. They were then a manageable length for thick bush, and the end of the first could quickly be jammed into the second and so on if it was too short. If they got wobbly the ends would be wrapped in flax fibre. That was from 'Lifeways of the Southern Maori' by J.H Beattie.