At the beginning of the game you get Pikachu and he Gets Eevee(Which is so unfair IMO). Later in the game he evolves it. What decides it? He chose Jolteon BTW.
If the player beats the rival at both Oak's Lab and the early optional battle at Route 22, Eevee evolves into Jolteon. If the player loses one of these two battles or passes up the Route 22 battle, Eevee evolves into Flareon. If the player loses at Oak's Lab, and loses or passes up the Route 22 battle, Eevee evolves into Vaporeon.
See Here for that information.
-Mike