How does a 1099 work?

Not sure if this belongs here or r/personalfinance/ but I just recently accepted a remote instructor position from a small private company in another state. I signed a formal agreement and I'm just waiting for the rest of the paperwork they'll send me however I'm unsure how a 1099 works.

I've heard you should put aside 30% of your pay for taxes but also that there are quarterly estimated taxes that I have to pay as well? I don't think I'll even break 1k of income from this to be honest (it's a part-time remote job I'm doing on the side as a student).

Can anyone guide me a bit on the steps I would need to take?

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