Let's Go simplifies evolution to three methods: reaching a level, using a stone, or trading. No friendship evolutions, no held items, no abilities, no breeding. The roster is 153 Pokemon: the original 151 plus Meltan and Melmetal (evolved through Pokemon GO only). Your partner Pikachu or Eevee cannot evolve.
Only three: reaching a certain level, using an evolution stone, or trading. That's it. No friendship evolutions, no held items, no time-of-day triggers, no location-based methods. Let's Go stripped the system down to Gen 1 basics, which makes sense since the Pokedex is limited to the original 151 plus Meltan and Melmetal.
Four: Kadabra, Machoke, Graveler, and Haunter. Same as Red and Blue. Give Haunter to a friend, it evolves into Gengar, they trade it back. No held items needed since the game doesn't have held items at all. Online trading works, so you don't need someone in the same room.
You can receive Alolan forms as in-game trades from NPCs in the Pokemon Center. These Alolan versions use the same evolution methods as their Kanto counterparts: Alolan Vulpix still needs an Ice Stone, Alolan Sandshrew needs an Ice Stone too. The method is the same, just the resulting type changes.