Okay, here's a (hopefully simple) way of explaining EVs and EV training:
Effort Values (EVs) are points that contribute to a Pokemon's growth as it levels up. Each time that a Pokemon defeats another Pokemon, it gains an EV for a certain stat. And everytime that stat recieves 4 EVs, it gives the Pokemon +1 to that stat when it levels up. Each Pokemon can recieve a maximum of 510 EVs in total, and each stat can accomodate 255 EVs. Only 252 points for each stat is recommended since it is the largest number in the limit that is divisible by 4. You can max out 2 stats this way by giving them both 252 points.
It is nearly impossible to keep track of your Pokemon's EV training. But keeping a pencil and paper ready to do so might actually help. There is a guide on Gamefaqs.com that shows you what EVs each Pokemon rewards you with and how many. The link is in the Sticky. (I've bookmarked it. The link, not the sticky. Lol.)
Now, for IVs...
Individual Values or IVs are values that a Pokemon's stats have when you first encounter that specific Pokemon. These points are randomly given to the Pokemon, and determine how high the Pokemon's base stats are. Each of the stats can have between 0-31 IVs. The higher the IV, the better the stat increase. IVs also determine the type and base power of each Pokemon's Hidden Power. This is why almost no two Pokemon of the exact same species, level, gender, or nature have the exact same Hidden Power. And don't worry if you want to find out what your Pokemon's IVs are but can't on your own. There are IV calculators all over the internet that you can use. It is advisable to use them when you freshly catch a new Pokemon that hasn't battled anything yet, or once your desired Pokemon from breeding has hatched. This way, you'll just have to enter "0" when the calculator asks for Effort Values (since you probably aren't willing to keep track of those anyway. I know I'm not :P).
Phew... Well, I hope I was able to help you in this way. Too bad the guy from whom I learned all this from has all of a sudden been banned. But, oh well.