WOLVES:
The domestication of wolves was a pretty smooth move by early humans. It started off with the wild wolves looking over to the humans, seeing their warm fires and cooked food. The humans took pity on them and gave them some leftover food of theirs, but the wolves kept coming back. These became the first domesticated dogs, which evolved and adapted to human lives from then on. In return of the free food the humans gave them, they protected the humans from other wild animals, kept them company, and helped hunt.
LIVESTOCK:
Later on, people found out they could farm animals. Instead of always moving around to find their food, they kept their food with them. This started the Agricultural Revolution. Instead of being nomadic and never being to settle in one place, humans bult permanent houses, build fences to keep in sheep, goats, etc. and bred them to keep supply. From then, they never had to worry about finding food again because they always had a fresh surplus of meat, crops, and materials.