I would say the (deceptively simple) core is getting expenses down, down, down. Learn to live well on very little. It's not only rewarding, but it's freeing as well.
After you do this for a couple years, track expenses, and log averages in a spreadsheet, you'll have a really good idea of what your retirement budget will look like.
For me, $250K is about what my "FU" threshold is. Once we hit that, our retirement budget works if we drop to a combined $15-20K part time income. We'd only be drawing $5K off our principal. But to have zero income at all, you need 25x your annual expenses (whatever that number is), which is a much bigger number as others have pointed out. In our case, it's about $700K based on my current projections.
The reason 25x (for a 4% withdrawal rate) is the key is because of the Trinity study. Read up on that. TL;DR, it's a number that survives in nearly 100% of historical situations.