In the more recent games, there are NPCs that you can talk to and they will tell you what type of Hidden Power your Pokémon has. According to Bulbapedia, the locations of the NPCs are:
- Platinum: Veilstone Game Corner
- Heart Gold/Soul Silver: Celadon Game Corner
- Black/White: Mistralton City
- XY: Anistar City
- South-Eastern-most house
- Also the location of the Hidden Power TM.
- Omega Ruby/Alpha Sapphire: Fortree City
- Top row of houses, second from the left.
- Also the location of the Hidden Power TM
If you want to find out through combat, here's something I threw together (Disclaimer: there's likely a much more efficient way to figure it out):
1. Battle a Patrat / Lillipup.
Super effective: Fighting. Didn't affect: Ghost. Normal effectiveness: goto 2
2. Battle a Cottonee / Petilil.
Super effective: goto 3. Not very effective: goto 4. Normal effectiveness: goto 5.
3. Battle a Klink.
Super effective: Fire. Not very effective: goto 6. Didn't affect: Poison.
4. Battle a Roggenrola.
Super effective: goto 7. Normal effectiveness: Electric.
5. Battle a Sewaddle.
Super effective: Rock. Normal effectiveness: goto 8.
6. Battle a Woobat.
Super effective: goto 9. Normal effectiveness: goto 10.
7. Battle a Ducklett.
Normal effectiveness: Grass. Not very effective: Water. Didn't affect: Ground.
8. Battle a Sandile.
Normal effectiveness: goto 11. Not very effective: Dark. Didn't affect: Psychic.
9. Battle a Ferroseed.
Normal effectiveness: Ice. Not very effective: goto 12.
10. Battle a Timburr.
Super effective: Flying. Normal effectiveness: goto 13. Not very effective: Bug.
11. Battle a Darumaka.
Normal effectiveness: goto 14. Not very effective: Steel.
12. Battle a Drilbur.
Normal effectiveness: Dark. Not very effective: Rock.
13. Battle a Trubbish.
Normal effectiveness: goto 15. Not very effective: Poison.
14. Battle a Deino.
Super effective: Dragon. Normal effectiveness: Normal. Not very effective: Dark. Didn't affect: Psychic.
15. Battle a Blitzle.
Normal effectiveness: Dragon. Not very effective: Steel.
My thought process (possible types at each stage) is in the revision history of this answer.
Feed him 11 Pomeg (lowering HP), Kelpsy (lowering Attack EV), Qualot (lowering Defense), Hondew (lowering Special Attack), Grepa (lowering Special Defense), and Tamato Berries (lowering Speed).
If a Pokémon has over 100 EVs in a stat, the EV-lowering berry will reduce it to 100 no matter how high it is, and after that, each berry will decrease the stat by 10 EVs after that. Because of this, feeding a Pokémon 11 of a stat decreasing berry will always result in 0 EVs in that stat.
This is assuming you can gain access to the EV berries. As far as I am aware, you can't find them in game yet. These berries are the only way you can decrease EVs.
Best Answer
Using the C-Gear's wireless function, you want to look for the Entralink. This will teleport you to a physical location in the game world that can only be accessed via the C-gear; it's counter-intuitive, but it's basically like the Underground from gen4. In this area, you'll have the option to catch pokemon befriended from the Dream World. This lets you capture them in whatever ball you want rather than being forced into using a standard pokeball. They're willing to be caught, it's not difficult.