What is the simplest way to play a sound or wav file?
Arduino will probably be the simplest option as I suspect there will be tons of various libraries and shields to do just that (3sec on google gave me the MP3 player shield from Sparkfun).

If you want to learn a bit in the process, and you don't mind that sounds will require pre-processing to be loaded onto the system, you could: read a WAV file into an array using any software of your choice, load that array into an EEPROM chip big enough for it, and use a counter to iterate through the content to play the song. Each tick of the counter you'll get a value, that needs to be sent to a digital to analog converter before feeding a small speaker (or a preamp). I did just that on an FPGA a few months back, using Matlab's wavread() function to get the EEPROM memory content.

Somewhere in the middle, you've got the MP3 decoder chips, for example from VLSI. The MP3 Arduino shield is based on that, and its schematic is available as usual on Sparkfun's website in case you want to adapt it for your own purposes.