You are on the right track in estimating 25% or so of your net income to send in as quarterly payments.
Quarterly payments are not legally required, but if you underpay you will be charged an underpayment penalty, which is like being charged 6% interest on your underpayment.
The IRS makes it easy to pay; just go to their website: Paying Your Taxes.
TurboTax has a good article on this: Estimated Taxes: How to Determine What to Pay and When.
@joshualwe
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