As a US citizen or resident, you are required to file a full US tax return to report your world-wide income.  If you are going to be overseas more than 330 days of the year, you qualify for the foreign earned income exclusion, which exempts your foreign earned income from US tax, but not your unearned income.  (Earned income is from working including self-employment, unearned income is dividends and interest and capital gains and so on.)  There is also a deduction or credit for foreign income tax paid.

So what you need to do is start by filling out a full schedule C the same as you would as if you were working in the US.  List all your income, all your expenses, and calculate your net profit.  

Open your return and search for self employed income (use this exact phrase). Select the Jump to link. This will take you directly to the section where you can enter info about your self-employment work, including any 1099-NECs or 1099-MISCs you have.  You may have to enter some info about your business if you haven't already provided that. You’ll also be able to enter any cash, personal checks, credit card payments, or cryptocurrency (Form 1099-K) related to your self-employment.

If you meet the requirements, you can exclude up to $100,800 in foreign earnings from your taxable income. You can also take a credit (or deduction) for foreign taxes paid.  However, you won't be able to take a credit or deduction for taxes paid (or accrued) on foreign earned income/housing that you excluded (because excluded income/housing isn't being taxed.

To enter foreign earned income in TurboTax, please follow these steps:

1. Click on Federal Taxes > Wages & Income  [If you're in TT Home & Biz:  Personal > Personal Income > I'll choose what I work on]
2. In the Less Common Income section, click on the Start/Update box next to Foreign Earned Income and Exclusion.  (See Screenshot #1, below.)
3. On the screen Did You Make Any Money Outside the United States? mark Yes and click Continue.  (Screenshot #2)
4. On the screen What Form(s) Was Foreign Income Reported On? mark the selection that applies and click Continue. (Screenshot #3)
5. Continue through the screens, entering the requested information.

For more information on the Foreign Earned Income Exclusion, see Foreign Earned Exclusion on the IRS website.

To enter foreign taxes paid, please follow these steps:

1. Click on Federal Taxes > Deductions & Credits [In TT Home & Biz:  Personal > Deductions & Credits > I'll choose what I work on].
2. Scroll down to the Estimates and Other Taxes Paid section.
3. Click on the box next to Foreign Taxes.  (Screenshot #4)
4. On the Foreign Tax Credit screen, click on the Yes box.
5. Enter the information requested on the screens. 

Once you designate it as foreign-source income you will then be able to determine if you can exclude it under the Foreign Earned Income Exclusion or take a credit for taxes paid on the same income to another country. 

To add to the other excellent answer you received, as a freelancer / self-employed individual, you need to pay self-employment tax based on the net profit on your Schedule C.  Self-employment tax is like the self-employed person's version of Social Security and Medicare tax that is paid by employees. This tax cannot be avoided using the Foreign Earned Income Exclusion or the foreign tax credit. That means, for example, that even if all of your earned income is excluded under the FEIE and you have no income tax liability, you could still owe a tax bill because of the self-employment tax. Many freelancers overseas are not aware of this and are surprised to find their tax return doesn't show a $0 balance due. 

The only way to potentially not be liable for self-employment tax while self-employed overseas is to be working in a country with a totalization agreement with Social Security and to participate in that country's social security system. In essence, that means you would be able to opt in to paying into the resident country's social insurance in lieu of paying into US Social Security. However, Argentina is not one of the countries where the US has a totalization agreement. You can find the entire list here:

https://www.ssa.gov/international/agreements_overview.html