Gig Work, Estimated Tax, and Withholding

I just started gig work as a side job back in June and am confused about if I need to pay an estimated tax for that. If so, how do I determine how much to pay or is that already determined by the IRS (and how would I find that)? Also, I do have a full time job that does deduct taxes and saw somewhere that I could have them withhold some to account for that. What is the easier option and how much should I withhold from my check if going through my employer? Thanks for your help!