That's the problem isn't it? That feeling gets rid of the 'why' to live. Asides from feeling obligated to others. As for how- by continuing on in whatever way you want to and not dieing. It's harder to know what direction to go in though when the 'why' is gone.
I just try to live so that things don't get any worse! I try to earn money from doing a job I find more rewarding and I distract myself as much as possible. Music, films, pod casts.
I'm guessing you still have preferences in life? I suppose they are interests. Would you prefer to do housework or, watch a film? I guess we all try to do as much of the things we want to but, it doesn't work out that way for a lot of us.
Are you NEET may I ask? Maybe that's a part of it. So- you have the time to do whatever you want but, maybe not the financial resources? I agree though. Even 20 years ago, I'd figured out that I wasn't massively interested in what life had to offer!