Can I file my own taxes?

The TurboTax program is do-it-yourself tax preparation software.  So you have to file the tax return yourself after completing the return.

You complete your tax return by finishing all 3 Steps in the File section. In Step 3, to e-file your tax return, you must click on the large button labeled "Transmit my returns now".

Go to this TurboTax website for the Free online edition - https://turbotax.intuit.com/personal-taxes/online/free-edition.jsp

Yes, you can do your own tax return on paper using the forms and instructions from the IRS, or you can use TurboTax to do your own tax return. 

DoninGA has explained how to use TurboTax Online to your return very well.

If you want to try to do it on paper, you will use Form 1040 and the IRS instructions, which are available here.