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You will report the income, along with any related expenses, on a Schedule C that you attach to your tax return. The "net" income (income minus expenses) will be subject to both income tax and self-employment tax. This reporting is only done once per year.
You should estimate the amount of tax that you will owe and make a payment using Form 1040-ES on 4 dates throughout the year - 4/15, 6/15, 9/15, and 1/15 of the following year. If any of the dates fall on a weekend or holiday, the payment is due on the next business day. So, this year the 9/15 payment is actually due on Monday 9/17. A good estimate would be 15% of the net income for self-employment tax plus 15-25% of the net income for income tax. The income tax rate will depend on your other income, deductions, etc.