The first step is to install the Haskell Platform, if you don't already have it. Then it should be enough to simply run
cabal install diagrams
By default this will give you
diagrams-core (core data structures),
diagrams-lib (standard library),
diagrams-contrib (user-contributed modules), and
diagrams-svg (native Haskell backend outputting SVG files).
diagrams-rasterific backend is also fully-featured and can output various raster formats; if you run
cabal install -frasterific diagrams
it will be installed as well.
There are also some very old installation instructions for the cairo backend; YMMV.