How do I log out of turbotax

Since the Online version is not yet operational then I assume you are using the Downloaded version ... so simply close the program to "log out" and you can choose to save your progress or not when asked.  

It's always a good idea to make a backup copy of your tax data file, in case your original gets lost or corrupted. Here's how:

1. From the File menu in the upper-left corner of TurboTax, choose Save As (Windows) or Save (Mac).
2. Browse to where you want to save your backup.
   • Tip:If you're saving to a portable device, save it to your computer first to prevent data corruption. Then, after completing Step 4, copy or move the backup file to your device.
3. In the File name field, enter a name that will distinguish it from the original tax file (for example, add "Backup" or "Copy" to the file name)
4. Click Save and then close TurboTax.
5. Restart TurboTax and open the backup copy to make sure it's not corrupted. If you get an error, delete the backup and repeat these steps.

If you make changes to your original tax return file, repeat these steps to ensure your original and backup copies are in-synch.

Related Information:                             

• Retrieve a Tax File from a Portable Device
• What's the difference between the tax data file and the PDF file?

AND save it as a PDF so you have access to a copy even if you don’t have the program still installed and operational :

• How do I save my return as a PDF in the TurboTax software for Windows?
• How do I save my return as a PDF in the TurboTax software for Mac?

AND protect the files :

• How can I protect the tax files on my computer?

Click on Sign Out at the bottom left of the online program screen.

The instruction to save my work and close Turbotax is "close the file"! To close a file I hit the "X" in the upper right corner.  When I do this I get the screen "Do you want to save this file?"! Of course I do! The first time I did this it had me save the file as "I gave it a name." The next time I wanted to save my work and close, I hit the X in the upper right corner and again I got the screen "Do you want to save this file?" I hit yes and it closed without asking me to name the file. Now everytime I close by hitting the X; it give me the choice to "save"; then I am done. 

That is the closing process for TurboTax Desktop.  The other answers are for TurboTax Online.  @fdchomesite