For the most part, it’s fairly easy to use the audio module. The one difference is that it is necessary to use certain pins on the Teensy for proper timing of the communications (different pins than library says to use for the Arduino).
To use the module, first download the file from the link I include at the bottom of this post. Install the library (and laugh at it’s absurdly long name). I also included an example program I made that uses the correct pins. (The example included in the library is more comprehensive but it has the wrong pins selected).
Next, (using a Windows machine) convert mp3s to the obscure format used by the module.
For some reason, I couldn’t get the program to use WAV files without being glitchy. Also, it’s important to check the option in the program to match the bitrate or something like that (you don’t want to change the bitrate).
After you convert the files, name them as consecutive numbers starting with 0000. Put them in the root directory of a microSD (NOT sdhc!) card.
Once you’ve done that, go ahead and connect the module to the teensy and load your program. You should have audio.
Now, I’ve only tested this with the Sparkfun model. The other one (which is smaller and cuter) ought to work the same way since it has the exact same chip powering it.