Collect 25 Eevee Candy
Tap Eevee in your Pokémon storage
Tap Evolve
Use the nickname trick once per Eeveelution:
Rename Eevee to Sparky for Jolteon
Rename Eevee to Rainer for Vaporeon
Rename Eevee to Pyro for Flareon
Rename Eevee to Sakura for Espeon
Rename Eevee to Tamao for Umbreon
Rename Eevee to Linnea for Leafeon
Rename Eevee to Rea for Glaceon
Rename Eevee to Kira for Sylveon
For Espeon or Umbreon, walk Eevee as your buddy for 10 km and evolve it during the day for Espeon or at night for Umbreon
For Leafeon, evolve Eevee near a Mossy Lure Module
For Glaceon, evolve Eevee near a Glacial Lure Module
For Sylveon, earn 70 Buddy Hearts with Eevee as your buddy and then evolve it
For other evolutions, evolve Eevee normally without a special method