I'm trying this right now. The game is one of those ball-and-platform games (use the platform to deflect the ball and hit the blocks). I'm not sure if I'll get an Umbreon or Jolteon.
Either way, once beating the 4 levels you can either keep the Pokemon you earned (I don't think you can choose, I'll get some more info as soon as I beat the game) or you can play again as many times as you like until you get the Pokemon you want. Once you choose to keep that Pokemon though, that's it. You can't change your decision.
Ahh, now I see how it works, kinda. I'll see better when Dream World goes online.
Anyway, as you play, some of the blocks will give out power-ups for the platform, and may also give out little balls containing a clue of which Pokemon this goes towards. When you catch the orb with the platform the shape of the Pokemon appears.
At the end of four levels, the orbs you collected are tallied and you receive the Pokemon that you got the most orbs for. You can choose to keep it or try again, it asks if you are sure you want to keep it after saying 'yes' once.
You need to be careful though, if you aren't looking for the first three evolutions (Jolteon, Flareon, Vaporeon) you can start gathering orbs for Espeon and Umbreon at level 3, but Glaceon and Leafeon don't appear until level 4, making it a little tough to grab the orbs for that Pokemon.