Meat comes from a variety of sources, most obvious of which is hunting game. It is done in one of two ways. Small game, currently represented by squirrels, can be "found" during scavenging the forest hexes with Squirrel Snare equipped. Larger animals, such as deer, are roaming the main map along other creatures and have to be killed in combat. All animals, big and small, once dead turn into a corpse item that can be butchered with a sharp tool to yield meat chunks of various sizes:

As despicable as it is, corpses of humans and monsters can also be carved into meat chunks and prepared to be eaten in the same fashion. For those who want to try and avoid cannibalism, a word of warning: all meat appears the same at first glance and you can never be sure where that meat found in a raider's bag came from. A closer inspection may be warranted.