I had the same problem, Houndoom.
When I first bought Colosseum, I thought that they would automatically
purify when you got their Shadow Meter does to zero, but they didn't...
The key was in the Colosseum Manual that came with the game...
(See - isn't it good to read manuals from time to time?)
You have to travel to Agate Village and into the Celebi Shrine (the big
cave under the village that can be accessed by going down the slope left
of the Pokemon Center).
When you reach the shrine, go to the stone, gray statue in the middle and
press (A). It'll tell you that one or more of your pokemon are about to
open the door(s) to their heart(s). Pick the Shadow Pokemon that's at 0
on the Shadow Meter and the Purifying Process will begin!
Quite annoying - have to go back to Agate Village everytime you want to
purify a pokemon...
When purified, your pokemon will regain all the moves it had previously
known and all the experience it had gained from you battling with it.
It'll also get a ribbon!