The stylesheets are based on the "old" (pre-2012) osm.xml stylesheet at http://svn.openstreetmap.org/applications/rendering/mapnik/osm.xml that used to be used for the "main" map rendering on http://osm.org/
You need a copy of the OpenStreetMap data on a PostgreSQL/PostGIS database (I'm using PostgreSQL 9.3) - either the whole world or for a specific area, e.g. from http://download.geofabrik.de/europe/british-isles.html
Put the data on a database using osm2pgsql: http://wiki.openstreetmap.org/wiki/Osm2pgsql
You also need the coastline data from OpenStreetMap which is distributed as a shapefile. Use the large split "Mercator" one from here: http://openstreetmapdata.com/data/land-polygons
Contours are a bit more involved. I use, for Great Britain, the set from Ordnance Survey Terrain 50: http://www.ordnancesurvey.co.uk/business-and-government/products/terrain-50.html
These can then be put into a PostgreSQL/PostGIS database using shp2pgsql with comes with PostGIS.
Once the data is ready, Mapnik (including its python bindings) needs to be installed. I'm using 2.3.0-dev (i.e. the current nightly builds) but 2.2.0 should work OK for creating PNGs at least.
The script at https://github.com/openstreetmap/mapnik-stylesheets/blob/master/generate_tiles.py to generate sets of tiles from the stylesheets.
Note the futurecity.xml stylesheet requires msttcorefonts - & you'll need to let mapnik know where these live, e.g. in the python script:
custom_fonts_dir = '/usr/share/fonts/truetype/msttcorefonts/'
The example images, using the XYZ map tile convention, have x=16090, y=10213, z=15. See http://wiki.openstreetmap.org/wiki/Slippy_map_tilenames for further details.