Overview of quarterly tax payments - questions

Basically, I would love answers to most of the questions on the event overview page: 

  • Why do I have to pay quarterly taxes and how can I avoid it?
  • Is there an income threshold for making quarterly payments? If so (and even if not), how much does one generally have to pay? 
  • I just have a side gig - do I really need to make estimated tax payments?
  • What’s the penalty if I don’t pay quarterly self-employment taxes?
  • Do I have to pay quarterly estimates to my state too?
  • And finally, could you point me toward good resources for getting started with making quarterly payments?

Thank you!