To evolve Eevee into Espeon, the method depends on the Pokémon game you are playing, but here are the main ways:

In Pokémon GO

• Set Eevee as your buddy.
• Walk at least 10 kilometers with Eevee as your buddy and earn 2 Eevee candies.
• Evolve Eevee during the daytime while it is still your buddy.
• Evolving during the day will yield Espeon, while evolving at night will yield Umbreon

In Main Series Games (e.g., Pokémon Black, White, and others)

• Raise Eevee's friendship (happiness) to a high level (above 220 pre-Sword/Shield or 160 post-Sword/Shield).
• Level up Eevee during the daytime (the game’s internal clock determines day vs. night).
• Eevee will evolve into Espeon if leveled up during the day with high friendship.
• It helps to have Eevee hold a Soothe Bell to increase friendship faster.
• Avoid Eevee knowing any Fairy-type moves, or it may evolve into Sylveon instead

In Pokémon Legends: Arceus

• Raise Eevee’s friendship to a high level.
• Ensure Eevee does not know any Fairy-type moves.
• Evolve Eevee during the daytime.
• This will cause Eevee to evolve into Espeon instead of Sylveon

Summary

• Walk 10 km with Eevee as buddy and evolve during the day (Pokémon GO).
• Increase friendship and level up during the day (main series games).
• Avoid Fairy moves to prevent evolving into Sylveon (Legends: Arceus and others).

This process ensures Eevee evolves into Espeon rather than any other Eeveelution.