There are a few ways to do it. The first will only work if you know EXACTLY what EVs your Pokemon has. If you just caught it, it has 0 EVs.
Also, if the Pokemon is a low level you will not know its exact IVs so cannot work out the type/power. In this case, you can either level it up loads with rare candies (save beforehand so you can reset afterwards and keep the candies), or enter a level 100 Wi-Fi battle.
Once the Pokemon is at least level 50, plug the numbers into an IV calculator like this one - click "Calculate Individual Values" then "Calculate Hidden Power". It should tell you the exact result.
The other way to do it is to try it out in the field. Save your game, then:
- Teach HP to your Pokemon.
- Find somewhere you can run into the same wild Pokemon (same species and type) a few times quite easily. Their level should be about the same or higher than you, you don't want OHKOs.
- Use HP on the Pokemon and look how much damage it does. Then use another Special move with a similar power if possible and compare. (It must be special-category otherwise you can't compare the effect of them.)
- Reset your game if it's not very powerful so you can keep the TM for someone else (not necessary in Black/White but you might want your old move back).
For example I tried HP on my Ampharos with Power Gem (power 70). I used both moves and HP did about half the damage so it must have been around power 30-35 - not very useful! Don't forget to take STAB and super-effectives into account.