I have an HP laptop running windows 7 and just purchased an Audio-technica AT-LP60-USB turntable that had Audacity software included. Audacity has been installed on the computer but I am trying to set up the turntable to play through a recording session on the computer speakers and the documentation I have in the manual is very different from what is showing up on my screen. The menu is different and the set-up on Audacity is different. Is there a current edition of documentation?

The current version of Audacity is 2.0.3.
You can check which version you have by looking in the Help menu > About Audacity.
If you have an older version it is highly recommended to update (see here for instructions:

The recommended Audacity installer includes the Audacity manual in its Help menu.