EV Training is a special training to help you make you Pokemon's stats more than usual, or more than it would be if you just left them in the Day-Care or used Rare Candies all the way through to get them to level 100. Anyways, an EV is an Effort Value, each Pokemon gives a certain amount of Effort Values to certain stats, 4 Effort Values make the stat increase by 1. Ex, a Patrat gives of 1 EV for Attack, so if I kill 4 Patrats, I get 4 Attack EVs, and the Pokemon who participated in all 4 battles would gain +1 in the Attack stat. A Pokemon can have a total of 510 EVs, and only 255 EVs in 1 single stat, giving you a chance to fully maximize 2 stats.
For IV Training, IVs are Individual Values, they are numbers that increase your stats, ranging from 0-31. The higher the IV, the higher the IV in each of your stats, the higher your Pokemon's stats will be. You just pretty much have to catch or breed Pokemon continuously until you get 31 IVs in the stats you need them to be in.