You will probably find the “Getting Started” section of the manual useful: http://manual.audacityteam.org/o/quick_help.html
You can also access that section directly from Audacity (assuming that you installed Audacity with the recommended installer): “Help menu > Quick Help”
In order to do all of the cool things that Audacity can do, it works using its own “project” format. When you “Save a project” Audacity will create a folder containing all of the audio, and a .AUP (Audacity Project file) that tells Audacity what to do with the audio data. The AUP file is NOT AN AUDIO FILE.
To create a normal audio file you need to “Export” from the Audacity Project.
“File menu > Export” will allow you to export the entire project in one of a number of common audio formats.
“File menu > Export Selection” will allow you to export just the selected part of the project.
The easiest way to make a “selection” is to click on the audio track and drag along the track.
Note that most functions in Audacity are only available while Playback and Recording is stopped. If you find that most options are greyed out, then you are probably “Paused” and not “Stopped”. Press the “Stop” button to stop playback/record.
For best sound quality, export in WAV format (default).
One of the most useful parts of the manual for finding your way around Audacity is the first page. (Help > Manual (in web browser).
Note that the you can click on the picture of Audacity on that page to go to the description of that part of the interface.