I didn't file my taxes last year. Can I file them now, and if so how do I get started? I also would like to file my current taxes as well.

The TurboTax online editions are only for tax year 2017 - https://turbotax.intuit.com/personal-taxes/online/

To complete a 2016 tax return using TurboTax you will need to purchase and download one of the 2016 desktop editions from this website to install on your personal computer - https://turbotax.intuit.com/personal-taxes/past-years-products/

A 2016 tax return can only be printed and mailed, it cannot be e-filed.