Tutorial modified from: http://felix.delattre.de/weblog/2014/03/02/how-to-install-tilemill-on-debian-jessie-testing

Install dependencies:

sudo aptitude install nodejs npm libmapnik2.2 mapnik-utils postgresql-9.3 postgresql-server-dev-9.3 postgresql-contrib-9.3 postgresql-9.3-postgis-2.1 imposm

Install dependencies for compiling tilemill:

sudo aptitude install git libmapnik2-dev python-gtk2-dev libwebkit-dev libsqlite3-dev

go to tilemill install directory, e.g.

cd /usr/local/share/ 
sudo su

obtain the latest version of tilemill:

git clone https://github.com/mapbox/tilemill.git
cd tilemill

or the latest release of tilemill:

TILEMILL_TAG="v0.10.1"
git clone https://github.com/mapbox/tilemill.git
cd tilemill
git checkout ${TILEMILL_TAG}

make command node available:

ln -s /usr/bin/nodejs /usr/local/bin/node

compile and install tilemill:

npm install

create a tilemill launch-script:

echo "#! /bin/sh
node /usr/local/share/tilemill/index.js" > /usr/local/bin/tilemill
chmod +x /usr/local/bin/tilemill

sudo -u postgres createdb -U postgres tilemill_austria
sudo -u postgres psql -U postgres -d tilemill_austria -c "create extension postgis;"
sudo -u postgres createuser -Upostgres --no-superuser --no-createdb --no-createrole tilemill
sudo -u postgres psql -U postgres -c "ALTER ROLE tilemill WITH PASSWORD 'tilemill';"

# tabellen rechte fixen
sudo -u postgres psql tilemill_austria -c "ALTER TABLE geometry_columns OWNER TO tilemill";
sudo -u postgres psql tilemill_austria -c "ALTER TABLE spatial_ref_sys OWNER TO tilemill";
sudo -u postgres psql tilemill_austria -c "ALTER TABLE geography_columns OWNER TO tilemill";

# daten einspielen
mkdir src/tilemill-osm
cd src/tilemill-osm
wget http://download.geofabrik.de/europe/austria-latest.osm.pbf
osm2pgsql -d tilemill_austria --username tilemill --host localhost --password --slim austria-latest.osm.pbf