Effort Values or EVs are gradually added to each stat as a reward for pokémon battling experience. Each pokémon you battle either in the wild or by battling a trainer or Gym leader in the game has an assigned Effort Value. Unlike experience points that are divided among all the pokémon in the battle and those with Experience Share, all the pokémon involved receive full share in EVs.
These Effort Values range in each stat from 0-252. The maximum total Effort Values counted towards each pokémon is 510 for all stats combined. For every 4 EVs in one particular stat, 1 point is added to that base stat. Since you need 4 EVs to add one stat point, the maximum EVs that can be used is 252 for each stat equal to 63 stat points. Similar to IVs these will be distributed as the pokemon grows in level until it reaches level 100.
Effort Values are still maxed out at 510 in this generation, but the cap for each category has been set at 252 preventing training up to the previous 255 and gaining unusable effort points. The Super Training screen on the 3DS will give you a visual tracking of your EV training and when the bar to the right has been filled, a biceped icon will appear above the training bag indicating that your Effort Values have reached their max. There is also a man at the Pokémon Fan Club in Laverre City that can tell you if you have reached your goal and award you with an Effort Ribbon.
In previous generations, Effort Values were awarded with the next level up making it impossible to add them through battling once a pokémon reached level 100. Now they are added after each battle
One neat trick if you want to know exactly where your training stands is to save the game and use a reset bag. Your current EVs will be displayed numerically before they disappear. Just soft-reset without saving after doing this.