I missed the October 17 deadline to file an extension. How can I do it with Turbotax?

There is only one extension available. You can't extend the filing again beyond October 17. If filed after that date, the return is late. If you are getting a refund, there is no consequence from filing late. If you owe taxes, there is a penalty for late payment. The IRS will calculate it and send you a bill after you have filed.

Did you start your 2021 return?   If you did not even start it, you will need to download the CD/download software:

https://turbotax.intuit.com/personal-taxes/past-years-products/

You may also want to explore purchasing the software from various retailers such as Amazon, Costco, Best Buy, Walmart, Sam’s, etc.

If you already started the 2021 return using online TurboTax:

 You will be able to access the return you started by using the exact same account and user ID that you used when you started it.   But you can no longer use online software for any further changes.

Online tax preparation and e-filing for 2021returns is now permanently closed.

Now it is too late to use online software or to e-file. If you have any changes/corrections at all to make to your 2021 return, you now have to complete it using desktop software, which you must download to a full PC or Mac  (not to a mobile device).Then you need to print, sign and mail it.

https://ttlc.intuit.com/questions/2559403-how-do-i-finish-a-prior-year-return-that-i-started-in-turbotax-online

If you already paid for your online software you can ask customer support for a download of the desktop software.

They are available from 5 a.m. to 5 p.m. Pacific time Monday-Friday.

https://ttlc.intuit.com/questions/1899263-what-is-the-turbotax-phone-number

If you are getting a refund, there is no penalty for filing late.  If you owe tax due, then file and pay the amount due as shown on the Form 1040, but expect a bill later from the IRS for the penalty and interest you will owe.  Only the IRS will calculate this—TurboTax will not calculate it.

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 that will track it, such as UPS or certified mail so you will know the IRS/state received the return.

Federal and state returns must be in separate envelopes and they are mailed to different addresses.  Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.