Download the source tarball from the MPD home page and unpack it:

tar xf mpd-version.tar.xz
cd mpd-version

Make sure that all the required libraries and build tools are installed. The INSTALL file has a list.

For example, the following installs a fairly complete list of build dependencies on Debian Wheezy:

apt-get install g++ automake autoconf \
  libmad0-dev libmpg123-dev libid3tag0-dev \
  libflac-dev libvorbis-dev libopus-dev \
  libadplug-dev libaudiofile-dev libsndfile1-dev libfaad-dev \
  libfluidsynth-dev libgme-dev libmikmod2-dev libmodplug-dev \
  libmpcdec-dev libwavpack-dev libwildmidi-dev \
  libsidplay2-dev libsidutils-dev libresid-builder-dev \
  libavcodec-dev libavformat-dev \
  libmp3lame-dev \
  libsamplerate0-dev \
  libbz2-dev libcdio-paranoia-dev libiso9660-dev libmms-dev \
  libzzip-dev \
  libcurl4-gnutls-dev libyajl-dev \
  libasound2-dev libao-dev libjack-jackd2-dev libopenal-dev \
  libpulse-dev libroar-dev libshout3-dev \
  libmpdclient-dev \
  libavahi-client-dev \
  libsqlite3-dev \
  libsystemd-daemon-dev libwrap0-dev \
  libcppunit-dev xmlto \
  libboost-dev \
  libglib2.0-dev
      

Now configure the source tree:

./configure

The --help argument shows a list of compile-time options. When everything is ready and configured, compile:

make

And install:

make install