So you want to learn about meditation? Well, not caring about anything is a great start. It's like the foundation of the whole not-caring thing.
Here's the thing: you don't need to care about stuff that doesn't affect you. Like, seriously, it's just not worth your time. Focus on the things that do affect you, and just... well, not care about the rest.
For example, let's say someone's cat died. You can either be all sad and worried about the cat, or you can just be like, "meh, not my problem."
Next Chapter: Letting Go of Attachment