Audacity does not have the capability of extracting a tempo through any of its menu options. Some basic math skills are required to be able to determine the tempo of a song. However, with a little bit of work, you can easily find the tempo of any song by using Audacity to help the process along. Computers, despite all of their advances, still are not able to automatically determine the tempo of a song. Humans are needed to ascertain this abstract concept.
Start Audacity and drag the song file into the program. This will open the file and allow you to view the wave file in the preview pane.
Start playing the song with Audacity and tap your foot to the beat. You can usually identify the beat by listening to the rhythm part. The beat must be an equally spaced tempo that can easily be identified. When you dance, you are usually dancing to the beat. Listen to the entire piece to see if the tempo slows down or speeds up.
Select 10 seconds of audio by clicking on the wave file in Audacity and dragging the cursor over approximately 15 seconds of time. Don't worry about an exact number while dragging. Just aim for an approximate length of time.
Use the bottom window pane to fine-tune the selection from step 3. There are two boxes which show the start and end of the selection box. In the second box, make sure the piece ends exactly 10 seconds after the number in the start box.
Press play and count the number of times you tap your foot over the course of the 10 second selection. If there is more than one tempo, you will have to do this for each section. Multiply the number of beats in 10 seconds by 6. This will give you the tempo in the piece. For best results, count more than once.