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.
If your Eevee has any other nickname, the evolution will be completely random.
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.