How do I figure out my total contributions to a Roth IRA before 2022? I retired in 2020 so stopped contributing then.

Your financial institution should be able to give you that information. 

Please be aware, if you had the Roth IRA for 5 years and are over 59 1/2 then you getting Qualified Distributions which are nontaxable and you will not need to know the total contribution (you can ignore the net contribution question in TurboTax). Your Form 1099-R will have code T or code Q.

Otherwise, you will need to check your documents or ask your financial institution as Bsch4477 mentions.

I took money out of my Roth in 2022. Then TurboTax asked me if I took anything out before then, which I did once in 2019. Then it asked me what my NET total contributions were and I have to answer that question as I don't see any way out. Do I go back and tell it I never took any money out? I've had this Roth over 20 years and I will be taking money out in the future too. What do I do?

It depends. As DanaB27 mentions, if you are over 59 ½ and have code T or Q in box 7 then you can ignore the net contribution question.   If that scenario does not apply to you, check with your plan administrator as the other posts advises.