You do not file quarterly tax returns. Only one tax return is filed each tax year reporting your total income and expenses for the year if you are a self-employed independent contractor. Schedule C is used to report your SE income and expenses which is included and part of your personal tax return, Form 1040.
Using the TurboTax online editions you will need the Self-Employed edition for your self-employment.
You can pay estimated taxes during the tax year using Form 1040-ES and the worksheets available in the instructions for the form - https://www.irs.gov/pub/irs-pdf/f1040es.pdf
Estimated tax payments can also be paid using the IRS payments website - https://www.irs.gov/payments
You can use TurboTax to assist in calculating the estimated taxes using the procedure in this TurboTax support FAQ - https://ttlc.intuit.com/community/tax-payments/help/can-turbotax-calculate-next-year-s-federal-estim...
quarterly estimated taxes are due 4/15, 6/15, 9/15 and 1/15 of the following year. should the date fall on a weekend or holiday you get until the next business day. you have to estimate you income and self-employment taxes for the year and pay 1/4 on each of those dates. there is also an annualization method where
income for each quarter is annualized taxes are computer and the the taxes are deannualized
for the 4/15 the income and expenses (including standard deduction are for 1/1 to 3/31
for 6/15 1/1 thru 5/31
for 915 1/1 thru 8/31
for 1/15 the entire year
if your asking how to compute these taxes. TT 2018 has an estimated tax section for 2019
there are also calculators available on the web but be careful. couldn't say if any are illegitimate, but if they ask for your SSN or other personal info avoid them