You don't need to care, not everyone has to be your friend. In the other hand, if you feel like this happens with everyone, consider that you may be a little bit self-centered and try to talk and bond with people around you, I mean, it's not that hard, try with some members of your family first ;) hope I helped!
You're probably not hanging around the right kind of people, or maybe you're just not talking about the right things. The key to friendships is common interests, and even if you don't think have a lot in common with a certain person, there's almost always a common ground.
Generally, when you're not interested in what anyone else has to say, it could be a sign of selfishness/self absorbed behavior. Are you bored? Is it everyone or certain people? When you said you don't know how to act, did you mean you're nervous/uncomfortable or having trouble focusing?
You don't have to care about everybody! That's why we have close friends and acquaintances. You would burn yourself out mentally if you cared about everybody and what they were saying! Some people just need to hear themselves talk and they honestly aren't wondering if you care or not because they just need a warm body to talk at!