Put:
(load-module "mpd")
into your ~/.stumpwmrc
Then you can use “%m” in your mode line format, as well as various commands defined at the end of the file.
You can customize the modeline format (mpd-modeline-fmt), the status message displayed by the command mpd-status (mpd-status-fmt; note that this is also used on the modeline), and the status message displayed by the command mpd-current-song (mpd-current-song-fmt). See the documentation for mpd-modeline-fmt for more information.
See The Music Player Daemon protocol for more details.