When you first install MPD, when you run it with a pulseaudio backend, you might encounter the following problem:
Apr 27 22:50 : exception: nested: failed to connect: Access denied
As pulseaudio ships and runs by default on most desktops, and is good once you've configured it correctly (opinion), you need to make mpd coexist with it. The reason you get the above error is that while MPD runs as its own user, pulseaudio runs as the user currently logged in.
The simplest solution is to make pulseaudio accept TCP connections, and let MPD connect to it that way. On the user side, add the following line to ~/.config/pulse/default.pa:
load-module module-native-protocol-tcp auth-ip-acl=127.0.0.1
Add the following to /etc/mpd.conf:
And viola! It works! Now download some of my music, add it to the MPD library, and rock on!
While you're at it, MPDroid is an excellent Android client for MPD. It even supports streaming over MPD's in-built web server.