While Audacity has a menu option to generate DTMF tones, it doesn't provide one to analyze them.
I have written a pair of Audacity plug-ins that allow you to analyze DTMF (and Bell MF) tone sequences. They can be used, for instance, to show the tone sequences in the Evan Doorbell recordings; indeed, that was precisely why I wrote them.
They can be a bit fiddly to use due to their adjustability, especially so for the MF detector; this is mainly due to the extensive filtering that is done to clean up the signal for detection.
The default settings are reasonable for most source material, but some material may be difficult to decode, so you may need to change them, especially if you see inaccurate results. Some recordings may have issues with distortion that make an accurate read difficult or impossible.
Copy the mf.ny and dtmf.ny files into your Audacity plug-ins folder. On Linux systems, this is usually /usr/share/audacity/plug-ins when using a pre-packaged version of Audacity. On Windows, it would normally be C:\Program Files(x86)\Audacity\Plug-ins (again for pre-packagedversions).
Once installed, load a recording into Audacity. Select the region you wish to analyze. DO NOT SELECT THE ENTIRE RECORDING. Choose the desired analyzer from Audacity's Analyze menu. Normally, the plugin will create a new label track with the results underneath your audio track. If you already have a label track and wish to use it instead, be sure to extend your selection into the existing label track.