Well, I'm sure the suggestions aren't correct... but never mind, I've seen this question crop up many times. Here's the real way.
For your starter Pokemon in XD, you have to do the Mt Battle challenge (and I'm saying this in case - in story mode), from beginning to end (all 100 battles), WITHOUT leaving, or changing your Pokemon or using the PC. You are allowed to save and turn off in-between, yes, but you can't leave the place once you start at the first set. All those conditions must be satisfied to get the starter Pokemon.
And you can repeat the process twice more for the other two starter Pokemon, by redoing the whole thing as well. :)
As for getting the Ho-oh in Colosseum, it's different. Firstly, you'd need to have had purifyed all 48 shadow Pokemon. Then, using a registered team, you need to beat Mt Battle in Colosseum mode (not story mode). You can use Pokemon from the GBA games, but you'll need to make sure you 'register' them first, that's all. NB you don't get anything from Mt Battle ingame in Colosseum, execpt for PokeCoupons, another Time Flute at the top, and if you DO do it in the same way to get a starter in XD, you would get a special ribbon for each Pokemon. The starter pokes in Colosseum are all obtainable in the story mode - one early on, and the other two via side quests after beating the main storyline.
Hope I helped. :)