These steps are identical for both v1 and v2 codec breakouts, even if the boards look a little bit different
You should hear your MP3 files in the headphones.
You can also run File->Examples->Adafruit_VS1053_Codec->player_interrupts. This example demonstrates playing files in the background using interrupts. This allows you to do other things in your sketch while the music plays!
With both examples, you can change the file names in the code to play different files - or even extend the code to search the SD card for files to play.
Frank Cohen has submitted a wiring diagram for the FilePlayer example on a Micro. See his code posted here as well: http://votsh.files.wordpress.com/2014/02/vs1053-arduino-micro-connections.pdf
Note: For paying sounds in the background using interrupts, connect DREQ to pin 3 and change the code to match.