How do I file past due taxes, for example, from 2015 and 2016?

You can not do 2016 and prior using Turbo Tax.  They only sell the last 3 years.  See,  https://ttlc.intuit.com/community/choosing-a-product/help/can-i-use-turbotax-to-prepare-or-earlier-tax-returns/00/26325

You might want to go to a local accountant or tax place if you have a complicated return.  For simple returns you can fill out the forms by hand.

You can fill out the blank forms for free.

Here are some blank forms & instructions for 2016

1040 https://www.irs.gov/pub/irs-prior/f1040--2016.pdf     

Instructions https://www.irs.gov/pub/irs-prior/i1040gi--2016.pdf

1040A https://www.irs.gov/pub/irs-prior/f1040a--2016.pdf    

Instructions https://www.irs.gov/pub/irs-prior/i1040a--2016.pdf

1040EZ https://www.irs.gov/pub/irs-prior/f1040ez--2016.pdf    

Instructions https://www.irs.gov/pub/irs-prior/i1040ez--2016.pdf

2016 Tax Tables https://www.irs.gov/pub/irs-prior/i1040tt--2016.pdf

Publication 17 Tax Guide for 2016 https://www.irs.gov/pub/irs-prior/p17--2016.pdf

Don’t forget your state.  And you will have to print and mail your returns.  So be sure to attach copies of your W2s and any 1099s that have withholding on them.  You have to mail federal and state in separate envelopes because they go to different places.  Get a tracking number from the post office when you mail them for proof of filing.

2015

Here are some blank forms & instructions for 2015

1040 https://www.irs.gov/pub/irs-prior/f1040--2015.pdf     

Instructions https://www.irs.gov/pub/irs-prior/i1040gi--2015.pdf

1040A https://www.irs.gov/pub/irs-prior/f1040a--2015.pdf    

Instructions https://www.irs.gov/pub/irs-prior/i1040a--2015.pdf

1040EZ https://www.irs.gov/pub/irs-prior/f1040ez--2015.pdf    

Instructions https://www.irs.gov/pub/irs-prior/i1040ez--2015.pdf

2015 Tax Tables https://www.irs.gov/pub/irs-prior/i1040tt--2015.pdf

Publication 17 Tax Guide for 2015 https://www.irs.gov/pub/irs-prior/p17--2015.pdf

Software for 2015 and 2016 is no longer available.   If you want the paper forms to prepare by hand, I will put a link here for them.   It is too late to receive a tax refund for any year earlier than 2017, so you will not receive a refund even if the tax form shows one.  If you owe tax due, you still have to pay the IRS.

https://www.irs.gov/filing/where-to-file-paper-tax-returns-with-or-without-a-

2015

Form 1040  https://www.irs.gov/pub/irs-prior/f1040--2015.pdf

Form1040 Instructions  https://www.irs.gov/pub/irs-prior/i1040gi--2015.pdf

Form1040A  https://www.irs.gov/pub/irs-prior/f1040a--2015.pdf

Form 1040A Instructions  https://www.irs.gov/pub/irs-prior/i1040a--2015.pdf

Form 1040EZ   https://www.irs.gov/pub/irs-prior/f1040ez--2015.pdf

2016 

Form 1040  https://www.irs.gov/pub/irs-prior/f1040--2016.pdf

Form 1040 Instructions https://www.irs.gov/pub/irs-prior/i1040gi--2016.pdf

Form 1040A https://www.irs.gov/pub/irs-pdf/f1040a.pdf

Form 1040AInstructions https://www.irs.gov/pub/irs-prior/i1040a--2016.pdf

Form1040EZ https://www.irs.gov/pub/irs-prior/f1040ez--2015.pdf

Form1040EZ Instructions  https://www.irs.gov/pub/irs-pdf/i1040ez.pdf

https://www.irs.gov/filing/where-to-file-paper-tax-returns-with-or-without-a-payment

Remember to prepare your state return as well—if you live in a state that has a state income tax.

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service to track it so you know it was received.   

Do not combine both years in the same envelope.   Mail them separately.

Form 1040EZ Instructions  https://www.irs.gov/pub/irs-prior/i1040ez--2015.pdf