On Form 1040-ES, you'll estimate your 2022 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 is April 15th, 2022.
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 2021 Tax Rate for line 4 for checking the 2021 Tax Rate Schedules Sheet. Since they make over $9,950 and less than $40,525, their tax is equal to $995 + 12% of ($20,000 - $9,950). Which comes out to be $2201 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 $903.08.