Evolution is always a major factor in Pokémon and it continues here. When you level up a Pokémon, it may evolve. What level it evolves in the main series determines what level it will evolve so a Charmeleon will evolve into Charizard at Level 36.
Pokémon that evolved in the main series through evolution stone or by trading have also got an evolution method here. It's simply through level. For example, Graveler evolves at Level 36
With Eevee, the evolution is determined based on the Power Stones attached. If only Attack Stones, it evolves into Flareon. If only HP Stones, it evolves into Vaporeon. If an equal mix, itevolves into Jolteon.
When you're in the section for Power Stones, you have the ability to toggle on the Everstone. This will allow for you to continue using the Pokémon without it evolving.