EVs (Effort Values) are like experience points you get for defeating Pokemon, but they go into the 6 stats of HP, Attack, Defense, Sp. Attack, Special Defense, and Speed. Every time you gain experience in battle, you gain EVs depending on the Pokemon you KO. For example, Patrat gives 1 Attack EV and Purrloin gives 1 Speed EV. Look up the Pokemon you should KO to suit your needs. For every 4 EVs you have in any given stat, that stat will be 1 point higher than it was without those 4 EVs. The maximum amount of EVs you can have in any stat is 255 (Since 255/4 has a remainder of 3, it's as good as 252 EVs).
For example:
Let's say my Jigglypuff, with 0 HP EVs resulting in an HP stat of 348 at lv. 100.
If that same Jigglypuff had 88 EVs in HP (88/4 = 22), that Jigglypuff will now have an HP stat of 370 at level 100.
Again, if that same Jigglypuff had 252 EVs in HP (252/4 = 63), that Jigglypuff will now have an HP stat of 411! Noticeable difference, no?
It should also be noted the max amount of EVs a Pokemon can have in total is 510, so you can essentially max out the potential of 2 stats. Also, the stat gains your Pokemon get from this are gradual. You won't be able to notice any changes right away, but as you raise your Pokemon's level higher, it becomes much more noticeable.
IVs (Individual Values) are kind of like EVs, in that they raise the stats of a Pokemon, but they cannot be changed. They range from 0-31 in the six stats. They are determined whenever a Pokemon is encountered or received. The higher the IV, the higher the stat.
For example:
Let's say a Jigglypuff with a 0 HP IV has an HP stat of 340 at lv. 100.
A different Jigglypuff with an 8 HP IV will have an HP stat of 348 at lv. 100.
Yet another Jigglypuff with a 31 HP IV will have an HP stat of 371 at lv. 100.
The difference is quite noticeable. Although difficult, try to aim for perfect IVs for your Pokemon. Those small difference in points can make or break a game.
That's the basics of it. I won't bore you with the details of in depth stuff. If you have further questions, just ask.