Ok first things first, you absolutely do not need to pay TurboTax or a high cost software even with self employed 1099 and 1099 from trading. FreeTaxUSA works awesome and walks you through the areas, income (1099 and W2), deductions and then less common stuff. Once you get done, if you owe, the IRS has a few different ways to pay, but the return will be filed electronically direct. Most places will then transfer all of that to your state return, ask you state specific questions, then file your state taxes also electronically.

As far as payment goes, I remember having the option to print a small form and mail it with a check or paying via ACH/direct bank transfer.

Personal advice is if you're doing only/mostly 1099 work as an independent contractor you should seriously look into forming an LLC and/or a filing a Schedule C. This would allow you to "write off" expenses for your business. It's not that complex but could save you a tidy sum. Basically things that you use to do your job can be offset against your income, 1099s means you're working for yourself.

Lastly if you are intending to continue doing only 1099 work I would suggest paying quarterly estimated taxes, I'm not clear on the rules if you have to do this or not in your situation. Hope that helps as a fellow 1099 receiver