In XY, there are generally two ways of going about 'changing their Pokémon's stats'.
First, they have to determine the purpose of the Pokémon in the team; whether it will act as a defensive role, attacking role, an 'annoyer', etc you can get lots of guides for building Pokémon teams on the internet and smogon university is one of the most popular ones.
When you know the purpose of the Pokémon, then you can proceed to build up the stats of that particular Pokémon though:
- Super Training
- Defeating Pokémon
There is indeed a hidden mechanic in Pokémon that players call EV (Effort Values) and this is what determines the final stat of a Pokémon. Any Pokémon can have a total of 510 EVs and a maximum of 255 EVs in any particular stat. The stat now will increase by 1 unit for every 4 units increase in EV, which means that you can have a maximum useful EV of 252 in any stat (the remaining 2 'waste' EVs can be put anywhere).
For example, if you want a speedy physical attacker, you will want to have 252 EVs in Speed, 252 EVs in Attack, and most of the time, players put the remaining 4 useful EVs in HP. This also means that the other stats have 0 EVs.
Now, before starting any training, you would therefore want to make sure that the other stats have 0 EVs, and this is made possible through Stat reducing berries (Kelpsy, Tamato, Pomeg, Qualot, Hondew, Grepa; each decrease a specific stats' EV and the description is pretty straightforward in the game), the Reset Bag and the Perilous Soup.
Super training regiments have different courses which increase the stat of the training Pokémon by 4, 8 or 12 EVs depending on the training level. You also get a training bag corresponding to the training undertaken, so that also helps in the training. Just make sure to keep track of the amount of EVs to maximise the effectiveness of EVs used.
In Pokemon XY, you now have the option to have horde battles, which I believe is another popular method among players to farm EVs. You need to look up the amount of EVs a particular Pokémon gives when it is defeated and decide on the species you want to grind on. Here also, you will have to keep track of your EVs gained.
Since we're speaking about EVs, there are some ways to get those EVs faster:
- Using vitamins (HP Up, Carbos, Iron, Calcium, Zinc, Protein). Using 1 gives a Pokémon 10 EVs in the particular stat, unless that Pokémon has above 100 EVs in that stat.
- Pokérus - This doubles the number of EVs gained when defeating Pokémon (obtained randomly when defeating wild Pokémon)
- Power items - (Power Brace, Power Lens, etc obtained by exchanging battle points at the Battle Maison) These add 4 EVs on the particular stat on each Pokémon defeated.
- Macho Brace - Doubles the EVs obtained when a Pokémon is defeated.
- Wings - These increase the EVs of any particular stat by 1 EV.