how do i train my pokemon for the pokeatholon...??..!!..

No idea. I never used the stuff and still managed to beat them all, most of them easily.

Just switch up the pokemon you are using depending on the event.
Example: for speed event, look in your box for your 3 pokemon with the highest speed
just keep in mind that the stamina and skill event have pretty much nothing to do with the stats used for the events

like what some of people above me said......let your pokemon drink some aprijuice......you can see just at the left side outside of the pokeathlon dome

Ok red apricorns strengthen power, lower stamina. Yellow ones strengthen stamina, lower skill. Blue ones strengthen skill, lower jump. Green ones strengthen jump, lower speed. Pink ones strengthen speed, lower power. White ones lower the chance of lowering preformance. Black ones strengthen the chance of lowering preformance. What I usually do is 2 of the color that strengthens what I want, 1 that strengthens what they weaken, and 2 whites. That was kinda confusing so here's an example:
Power juice: 2 reds, 1 yellow, 2 whites.
This will not always work but it is pretty reliable! If u aren't sure test it on a Pokemon with only neutral preformance (yellow stars) and u wouldn't use.