I'll just paste some stuff that I gave to someone else a while back...
EVs are the abbreviation of effort values. A Pokemon has EVs between 0 and 252 in six different stats: HP, Attack, Defense, Special Attack, Special Defense, and Speed. All Pokemon start out with 0 EVs in each stat, but they acquire EVs for each Pokemon they earn experience from defeating. EVs boost a Pokemon's stats, but it's not a 1:1 ratio. At level 100 the EV to stat bonus ratio is 4:1, and at lower levels it takes more EVs to impact a stat. Pokemon in their first stage of evolution give 1 EV, Pokemon in their second stage give 2, and third 3. Pokemon without evolutionary lines tend to vary in EV yield. The EVs are generally all in a single stat, and what you get is consistent with each evolutionary family. A Gulpin will always yield 1 HP EV, and a Swalot will always yield 2 HP EVs. Now, while a stat can have up to 252 EVs, a Pokemon cannot have more than a grand total of 510 EVs. Obviously, getting all 510 EVs you want would take a while like this. But there's ways to speed it up. On rare occasions, (Think 1 in 20,000) a wild Pokemon will have what's called the Pokerus. Pokerus doubles the number of EVs you get from battle, so a Pokemon with the Pokerus that defeats a Gulpin will get 2 HP EVs instead of one. In addition to this, there are hold items called power items, the power weight, power band, power anklet, power belt, power lens, and power bracer. When a Pokemon holds one of these, its speed is halved, but whenever it gets EVs from a defeated Pokemon, it gets a bonus 4 EVs in a specific stat, which is specified in the item's description. In other words, a Pokemon holding the power weight with Pokerus can get 10 EVs from one Gulpin. But with the addition of horde battles, you can battle five Gulpins at once, and get 50 HP EVs from one horde. This is called Horde training, and it's the fastest method of EV training.
A great guide to this can be found here:
http://www.smogon.com/forums/threads/a- ... s.3490052/Now, prior to gen 6, you would have to keep all EVs in memory, but with the addition of super training, there's a graph you can refer to that shows a rough indication of a Pokemon's EVs. The green on the graph is a Pokemon's base stats, and the yellow is its EVs added onto the base stats. You can also do super training as a method of EV training, it's more concise and generally easier to not mess up, but it's also much slower. It can take well over an hour to EV train a single Pokemon that way, whereas horde training can take as little as 10 minutes.
If you have any questions, feel free to ask.
Also people can feel free to correct me on stuff, or add to this.