To learn how to not give a fuck about anything, you must realize that suicide is always an option if things get too rough to handle. No use enduring something that ain't worth it.
Once you get rid of the idea that life is something to be enjoyed and replace it with the idea that life is boring, tedious, painful and scary, it's much easier to not give a fuck about anything. In fact, suicide is probably the most rational action that many people could make.
So basically if you really don't want to give a fuck, you'll learn to not take your life so seriously and live in the moment, knowing that at any moment you could be thrown into a 180 and start taking seriously the idea of killing yourself. Live on the edge, take risks, don't wear your seatbelt, give most of your money to charities cause you don't need it, expect the worst and prepare for it, always keep the possibility of suicide in the back of your mind to ground your decisions, etc. Soon you'll learn to enjoy what you do have and not worry about losing it, since if you do lose it all you can always kill yourself. You'll also realize that death is not something to worry about or fear, since once you're dead you won't know what you're missing and you might even be avoiding a lot of really shitty experiences. Pretty simple, really.