Most Helpful Girl
It's really just a mindset. As soon as you catch yourself starting to care to much, try to think about what happens if it goes wrong. You don't die, the world won't end. If that person hates you, you have one less person in your life. Nothing to worry about, you did fine before you met them. If that event sucks, it is just one day of your life. There are 365 in a year, it's really not that important.
Practise this, it will get easier. Of course you'll still care about important things, but the little things you care too much about you can filter out.1
Most Helpful Guy
I want you to look at this image. This image was taken with the Hubble telescope, one of the most powerful telescopes humanity has ever built. All those dots represent stars, but not how you'd think. No, because each dot is a collection of stars, galaxies. We inhabit but one impossibly small corner of one of these enormous collections of stars that itself is sequestered away in an impossibly small corner of this vast universe. More than likely alone, and even if we aren't it's not likely we'll meet our universal neighbors.
It is in this impossibly small corner that we bicker among one another, fight and cry and cheat and steal and care and love and live and die. All that drama, taking place on what the rest of the universe may as well consider an atom. Or as the great Carl Sagan once put it "a fraction of a dot." So small is our influence in this universe that we may as well not be here. And as such, every and all actions that we as people do from here to our inevitable doom will be but a brief flicker in the universe's vast, nigh-immortal existence. Here and gone in a universal instant.
With that in mind, take solace in the fact that the universe is the unopposed master of not giving a fuck, and learn from it's beautiful mastery.6