The first step is to install the Haskell Platform, if you don't already have it. You will also need to have gtk and cairo (along with development headers) installed through your operating system. After that, it should ideally be enough to run
cabal install gtk2hs-buildtools diagrams
This will probably work under Linux/Unix but some workarounds may currently be required on Windows or Mac OS X; see below. Please edit this page to add information about any problems you encounter, workarounds you discover, etc.
Installing on Linux/Unix
As far as we know there are currently no issues installing diagrams on Linux/Unix systems.
Installing on Windows
Cairo can unfortunately be difficult to install on Windows.
Here are instructions for installing gtk2hs on Windows. They work with the exception of the issue described here, which can be circumvented by passing the --global option to 'cabal install cairo' (if you don't mind installing cairo in the global package database).
Here is a discussion about the most recent difficulties.