Lying flat is a very simple concept. All it is, in a nutshell, is refusing to participate more than you absolutely have to. It's a form of protest.
What it looks like is building yourself a little emergency fund and then cutting your hours at work down to the bare minimum that you need to maintain yourself. So working just enough to eat, have shelter, and all of your necessities. You won't really be buying much and you won't really be going out on the town much, but it sends a message if enough people do it.
It's a way of protesting a system. The reality is that we all have to work right now because the system won't allow us not to. That sucks. So we can protest it by lying flat and refusing to participate in this shitty system (shystem!) more than we have to. This puts financial pressure on the system to change, especially when our government sees 25%+ fewer tax dollars coming in.
Everybody's “lying flat” will look different. Single adults can lay much more flat than a single parent, for example. It'll depend on your basic needs and your ability to save up a small emergency fund.
Personally, I will be going down to working 3 days a week soon.