You start paying estimated taxes in 2020 for the income you are earning in 2020.
The due dates for you 2020 estimated taxes are:
First estimate for January 1- March 31 7/15/2020 (normally 4/15, but extended this year for COVID --19)
Second estimate for April 1-May 31 7/15/2020 (normally 4/15, but extended this year for COVID --19)
Third estimate for June 1 - August 31 9/15/2020
Fourth estimate for September 1 - December 31 1/15/2021
If you are making estimates for the additional taxes for the new self-employed business only (i.e., otherwise your taxes are sufficiently withheld), to estimate the amount you owe for the new business, you calculate your net income for each of those periods (income minus expenses) and then multiply that income by a percentage to get the amount to pay.
Your percentage for estimated taxes is equal to your (Income Tax rate + SE Tax rate - (Income Tax rate x SE Tax rate x .5) ). So, if you are in the 12% tax bracket for this additional income, your percentage would be approximately (12 + 15.3 - (.12 x .153 x .5) = 26.4%). That little subtraction in the formula is because you get to deduct as an adjustment to income half of your SE tax.
See this IRS website for FAQs related to estimated taxes.
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