Ask HN: How to find a better job while being employed?

I wonder, did anyone else ever had this problem. I have a full time job, but I also want to look for a better job. I can't just quit because I have a family and honestly, we wouldn't last a month...

So how can I look for a job? I'll have to answer phone calls during working hours from my current work place, and I will have to go to job interviews. Is this even possible without quitting or letting the employer know?