Catch an Eevee
Set Eevee as your buddy
Walk 10 km with Eevee as your buddy
Earn 2 Eevee candy while Eevee is your buddy
Evolve Eevee at night
Make sure Eevee is still your buddy when you evolve it
If you have not used the name trick before, rename Eevee to Tamao and evolve it once for an Umbreon
After the name trick is used, use the buddy method for additional Umbreon evolutions