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 now works with the Generation IV evolutions Leafeon and Glaceon.
When renaming Eevee the first time, the evolve button with display the evolution it will evolve into rather than a question mark.
Linnea to evolve into Leafeon Rea to evolve into Glaceon
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.
gaming.stackexchange.com/users/274/Brant
By default, when you evolve an Eevee in Pokémon GO , the evolution is chosen randomly from the set of potential "eeveelutions".
Evolution stones as you know them (water, fire, etc.)
don't exist in the current version of Pokémon GO .
Edit : There also seems to be a method for forcing a specific evolution by giving your Eevee a certain nickname before it evolves.
See @Brant's answer for more details .
gaming.stackexchange.com/users/81131/pushasha
Normally, evolving an Eevee will randomly result in either a Vaporeon, Jolteon, or Flareon with a 1/3 chance of either of them.
If you keep Eevee as your buddy for 10km, earn at least 2 candy with it
whilst it's your buddy, and then evolve it whilst it's your buddy,
it will evolve into either: Espeon
if evolved during the day.
Umbreon if evolved during the night.
It is day if the game screen in overworld and when catching Pokemon is bright, and night if this screen is dark.
The times when the game screen changes varies depending on your GPS and time location.
If you purchase a Moss Rock from the Pokemon shop (for 200 coins), place it on a Pokestop, spin the Pokestop, and then evolve Eevee whilst in the radius of the Rock, it will evolve into Leafeon .
The same applies for Glaceon with an Icy Rock.
The silhouette of Leafeon/Glacoen will appear if these requirements are met prior to evolution - if it doesn't, the requirements are not met and it would evolve into Vaporeon/Jolteon/Flareon.
You can also choose a nickname to force a specific evolution as per this answer - it only works once per nickname/evolution.
gaming.stackexchange.com/users/219593/MBorg
According to this site , stones are available after the gen 2 update.
Other than the naming tricks, there are other ways to control some evolution forms:
Walk with the Eevee for 10 kilometers and stay it as your buddy, then evolve it during: day – Espeon
; night: Umbreon.
There may be other better ways to control evolutions, but haven't been found out by all trainers.
gaming.stackexchange.com/users/172595/333-blue
In addition to the first three evolutions mentioned by @Brant, with the addition of the second generation there are two more Eevee names that will trigger a guaranteed evolution once: Tamao for an Umbreon.
Sakura for an Espeon.
gaming.stackexchange.com/users/57810/Dom
So I just caught an Eevee. Now, I need 25 candies to evolve it. The fact is that in the GameBoy color versions, that Pokémon needed a stone to evolve instead of experience. Depending of the stone he was fed with (thunder, water or fire), he was evolving in a different Pokémon.   Is the stone feature also in Pokémon Go? If not, what decide the evolution of this Pokémon?   Bonus point : If it's possible, how can I get a stone?
I caught an Eevee, which of its evolutions will it evolve into?
gaming.stackexchange.com
<pokemon-go>
gaming.stackexchange.com/questions/272930
gaming.stackexchange.com/users/149081/Jouramie
Sparky  to evolve into  Jolteon, Rainer  to evolve into  Vaporeon, Sakura  to evolve into  Espeon and Tamao  to evolve into  Umbreon.  While the evolving process happens randomly there are ways you can influence what it will evolve into. Changing its nickname is one of these, or evolving it in proximity of certain types of rocks.
User suggests that changing its nickname to a particular thing will make it evlove into that. Users suggest that rocks influence the evolving The evolving process happens randomly however.