Professions come from workstations
An unemployed villager takes the profession of a nearby unclaimed workstation: lectern = Librarian (enchanted books), composter = Farmer (crops for emeralds), barrel = Fisherman, smoker = Butcher, cartography table = Cartographer (explorer maps). Break and replace the workstation to reroll the offers until you get the trade you want — do this before any trading, because offers lock in after the first purchase.
The classic emerald engines
Farmers buy wheat, carrots, potatoes and beetroot — a working wheat-and-carrot farm literally prints emeralds. Librarians sell Mending and other top-tier books. Fletchers buy sticks (craftable from any wood) in huge volumes, which is the lowest-effort early emerald source in the game.
Curing for permanent discounts
A zombie villager cured with a weakness potion and a golden apple re-enters the village with massive permanent trade discounts — high-level books can drop from dozens of emeralds to one. The discount applies to every player on the server and stacks with Hero of the Village. It is the single most powerful trading mechanic in the game.