I would like to start setting aside money for my NEC taxes for 2022. How much should I set aside each month or whatever? So far ,this year I have earned6376.

I suggest using the following link to calculate your withholding (Form W-4)

https://www.irs.gov/individuals/tax-withholding-estimator 

You can either set the money aside or have your employer withhold for you.

If you do not have your employer withhold taxes, you should file Quarterly Estimated Taxes

so you do not encounter late payment penalties.

See  https://www.irs.gov/businesses/small-businesses-self-employed/estimated-taxes 

Perhaps another reviewer can explain the steps to have Turbotax do this.

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You can divide your tax on line 22 of your form 1040 by your taxable income on line 15 to get an estimate of your income tax rate. Then, add that to your self employment tax rate of about 15% and multiply the total by your net self-employment income (after expenses) and that will give you an idea of how much estimated tax to pay in. It may be a little high since this may not take into consideration all the credits you are entitled to.