If you're an astute Internet user: congratulations. You already kinda know the trick, thanks to this article's URL.
If you don't well, no sweat. That's what the rest of this article is for.
For a while, it seemed as if your Eevee's evolution -- assuming you find enough to evolve it -- was a matter of chance. In the original Game Boy games, exposing your Eevee to a stone determined its final form: a Water Stone begat Vaporeon; a Thunder Stone begat Jolteon; and a Fire Stone begat Flareon. Some Pokémon Go players speculated this game's evolution correlated with which attack your Eevee began -- that Dig resulted in Flareon, etc., etc.
But redditors, as they are wont to do, came upon a solution that harkens back to the original TV cartoon. As laid out by OP smithnigel, the original Eevee trainers were named "Rainer, Pyro, Sparky," and "they owned a Vaporeon, Flareon and Jolteon respectively."
If you name your Eevee one of those names, its evolution corresponds:
- Sparky for Jolteon
- Rainer for Vaporeon
- Pyro for Flareon
In the comments, another redditor posted a video showing the evolution on his phone as it happened, just to document the situation.