If you paid by credit card the card statement will have your payment.

To access your current or prior year online tax returns sign onto the TurboTax website with the userID you used to create the account - https://myturbotax.intuit.com/

Scroll down to the bottom of the screen and on the section Your tax returns & documents click on Show.  Click on the Year and Click on View order details

Use this TurboTax website to check your orders and payments - https://shop.turbotax.intuit.com/commerce/orderstatus/orderstatus.jsp

This link is for the online product.  Where can I find an invoice for the downloadable product, purchased through TurboTax advantage?

Sign into your advantage account ...  https://ttlc.intuit.com/community/choosing-a-product/help/how-do-i-update-or-confirm-the-info-in-my-...

It's nearly impossible to find.  You have to navigate to order status then type in the order number which is only on the physical package that arrived in the mail.  There is no order number or invoice on the website otherwise, and no invoice was sent by email.  Intuit needs to get their act together on this.

The original question was how to print or save an invoice showing the credit card charge, shipping info, etc. I have the same question: how do I find a document, generated by TurboTax or Intuit, stating the amount I paid and where it was shipped, etc. The credit card companies do not provide that information; they simply show a charge and the date. 

An email should have been sent ... however since the cost is no longer tax deductible an invoice is really not needed.  

It absolutely is tax deductible if you have a business.

The CC statement for a payment to Intuit  should be sufficient for your business if you use the BUSINESS version ... however if you use one of the Personal versions you can only take the difference in costs from the Deluxe version and the Self Employed version (for your Sch C) ... you should have made a note of the difference in price last year and saved the email receipt with that note on it.  

If you still need help ... 

Use this website to contact TurboTax support for this situation:

https://support.turbotax.intuit.com/contact/
Support can also be reached by messaging them on these pages https://www.facebook.com/turbotax/ and https://twitter.com/TeamTurboTax

I want a completed invoice for my state return costs of $19.99.  I normally receive an email that I can print.  This time nothing, except my card being charged.  When I go to Turbo Tax website it only lists what I have bought--no costs, nothing.

How to review your fees: https://ttlc.intuit.com/questions/2565973-how-do-i-review-my-fees-in-turbotax-online