Lots of people seem to misunderstand EVs, one of the core factors for building your own battle-ready Pokemon. So let me talk about this obscure, but very key, feature.
What are EVs?EVs, or Effort Values, are a hidden stat that all Pokemon have. A freshly-caught/obtained Pokemon always has zero EVs in all stats. As your Pokemon battle other Pokemon, they gain EVs in addition to experience points, which will improve your stats. But hold on! Not all EVs are equal; there's a limit to how many a Pokemon can have at a given time, and you want them applied to the stats that are most important to your Pokemon, don't you?
How do you get them?Every time your Pokemon is eligible for EXP from a defeated Pokemon (including when the Pokemon switches out or uses the EXP Share, and including when the Pokemon is level 100, but not including when the Pokemon faints), the Pokemon gets EVs. What EVs you get are determined by the species of the enemy Pokemon; generally speaking, weak or unevolved Pokemon give 1 EV, strong non-evolving Pokemon and Pokemon that have evolved once give 2 EVs, and legendary Pokemon and Pokemon that have evolved twice give 3, and they usually (but not always) apply the EVs to the stats that the enemy Pokemon excels in. You get EVs when fighting both enemy trainers and wild Pokemon.
You can also use Vitamins to instantly gain 10 EVs in a stat, but Vitamins only work up to 100 EVs. You can also use Wings, which work beyond 100 EVs but only give EVs one-at-a-time, meaning you'll need a lot of them.
The sixth generation introduces a new method: Super Training! Now not only can you punch bags and play a soccer-themed minigame for EVs, you can even see a chart that shows your overall EV total!
How many can you get?Each Pokemon is limited to 252 EVs (255 in previous gens) in one stat and 510 EVs overall. Once they reach these numbers, they will stop gaining EVs. (Recall, Vitamins stop working when you reach 100 EVs in the corresponding stat.)
Since EVs only work in groups of 4, in previous gens you'd be best off stopping at 252 EVs instead of 255 - but now? 252 is the max anyway, so don't worry about it.
How exactly do they work?Most people will tell you that four EVs provide one stat point. And at level 100, with a neutral nature, this is true!... but non-neutral natures will skew it a bit, and the effects are less pronounced (but still absolutely present!) at lower levels.
As for the stats themselves, a common misconception is that they are the culmination of a bunch of "stat gains" granted at level up. This isn't true! "Stat gains" do not exist in Pokemon! Oh, you see Little Plus Numbers (henceforth LPNs) when you level up, but these are unimportant and you're actually better off ignoring them! No no, stats are calculated by formulae (round down at every step):
HP = ((Base * 2 + IV + EV/4) * Level / 100) + Level + 10
Stat = (((Base * 2 + IV + EV/4) * Level / 100) + 5) * Nmod
Base = determined by Pokemon species, or sometimes forme. This only changes upon evolution or forme change.
IV = Another hidden stat that is static and determined when you get the Pokemon, ranging from 0 to 31 in each stat. You can't change this.
Nmod = 0.9, 1.0, or 1.1, depending on the Pokemon's Nature. On the status screen, most Pokemon will have one stat tinted red (that one gets the 1.1) and one tinted blue (that one gets the 0.9). Some Natures do not affect stats at all. No Nature affects HP.
Please don't make the common mistake of thinking that Pokemon under level 100 get no benefit from EVs! As you can see if you work out the math, a level 50 Pokemon will gain a stat point after every 8 EVs - half as much benefit, but still useful.
Creator of Jay's Journey (see quote!)
"It's not ten years old! Therefore, it sucks!" - Nostalgia whores everywhere