According to this post on the /r/pokemongo subreddit, you can force your Eevee to evolve a certain way by changing its nickname before evolving it to:
- Pyro to evolve into Flareon.
- Sparky to evolve into Jolteon.
- Rainer to evolve into Vaporeon.
(These are the names of Eevee Brothers from the TV series/Manga)
You can also, as of the Generation II update, use nicknames to evolve into a certain Eeveelution, but like before, this works only once.
- Tamao to evolve into Umbreon.
- Sakura to evolve into Espeon.
This technique will only work once per evolution. For example, if you have already evolved an Eevee named Rainer into a Vaporeon, evolving another Eevee named Rainer will result in a random evolution.
Evolving without the naming tricks will give you Flareon, Jolteon or Vaporeon by random chance.
Also, according to another reddit thread, by walking 10km with Eevee as a buddy you will get Espeon when evolving during the day and Umbreon when evolving during the night.
