On Form 1040-ES, you'll estimate your 2020 income and then pay taxes on a quarter of what you expect to make. The IRS will want you to make quarterly tax payments if you expect to owe $1,000 or more in taxes on your income from a given year.
However, if this is not your first year filing taxes as an independent contractor, then you'll be expected to pay the same amount in taxes as you paid last year.
Additionally, requirements on quarterly taxes can be found here.
Note: The first quarter estimated tax deadline has been moved to July 15th, 2020. The IRS has made this change and others in response to the COVID-19 pandemic. Follow the link here for more information on the IRS date changes.
Here's an example of a Form 1040-ES, filled out by a rideshare driver that files single, makes $30,000 adjusted gross income and, has $10,000 in deductions. This means their taxable income is $20,000.
This rideshare driver calculated their 2020 Tax Rate for line 4 for checking the 2020 Tax Rate Schedules Sheet. Since they make over $9,875 and less than $40,125, their tax is equal to $987.50 + 12% of ($20,000 - $9,875). Which comes out to be $2205.50 on Line 4 of the 1040-ES
Then this rideshare driver used the Self Employment Tax and Deduction Worksheet to figure out their self-employment tax amount for Line 9 of their 1040-ES. On Line 10 of the worksheet below, you can see their self-employment tax comes out to be $903.07