Handy dandy chart for reference.
Natures are, by far, the easiest aspect to control. All you need is a pokemon with Synchronize as an ability, and the nature you'd prefer. Put one as your lead pokemon, and there's a 50% any pokemon you catch will have that nature. Of course, the game does not tell you this (Boo!), so it's not exactly obvious. That's really all you need to know about natures.
Now, for my closing remarks:
First off, be assured that you do not need to know any of this stuff in order to play single player. You can beat the Elite 4 with any pokemon you want to use. These are only things you need to know if you are going to play the game competitively. With that said, I will agree with Mr. Sterling that Nintendo should have made more of an effort to make people aware of these aspects. As it is, they make you rely on the internet far too much. Should they be removed from the games? No, I do not think so. While slightly annoying, they give you a reason to work for your team. They make you train, and it can be satisfying to see the fruit of your efforts. Pokemon is not a worse game because of these aspects, but it certainly is not for those who are not dedicated.
LOOK WHO CAME: