How exactly does re-districting work?

[Lief 🗽]

The last time this happened, I was eleven years old and didn't really pay attention/know what redistricting even was. So how exactly is it done? In most states, the state legislatures are in charge of it. Does the majority party hire a couple of demographers/cartographers and tell them to put something together for them? Are a couple different plans put forward? Do the legislators take an active roll in map drawing? I assume the nitty gritty of precinct populations and all that is beyond the interest/knowledge of most state legislators. Are we going to see the maps on the internet or something before they're voted on? If the Justice Department or other groups sue, how long does it take to settle that usually?

I mean, it's one thing to draw up maps on our computers as a hobby, but I'm curious how the actual process of census results to new districts actually works in practice.