You will need a copy of Pokémon Black 2 or White 2 to catch Eevee.It is not possible to get Eevee in either black or white.You can only get Eevee by trading or the Dream World.
Step 1: You can go to Castelia City.
You can reach the big city by boat.This is the only place where you can catch Eevee.
Step 2: You can buy a lot of Poke Balls.
Eevee has a low catch rate.
Step 3: Next to the entrance is a pier.
Step 4: Go down the stairs on the small deck once you reach the pier.
If you haven't been here before, your rival, Hugh, will be there as well.After that point in the story, be sure to come here again.
Step 5: Follow the path until you see a left turn.
Go up the stairs if you see them.
Step 6: There is a small garden with a tree.
The guy says that it was the beginning.
Step 7: You need to walk through the grass.
There is only a 5% chance of Eevee appearing in the grass.
Step 8: Don't give up.
It may take a while, but eventually you will find one.Only then will you be able to catch it.Only level 19 is where you can find it.
Step 9: Lower its health to about 7% when you're fighting it.
You can put a Poke Ball on it.Be patient, you're unlikely to catch it first time.An Ultra Ball has a higher catch rate.