GNOME-DB used to be composed of several components, not all of them being mandatory: libgda, libgnomedb, and mergeant. All of these components have been grouped into one single source package with optionnal compilation of the UI part (so it's still possible to restrict the compilation to the core, non UI part).
libgda has been developped primarily on a Linux OS, but should compile and run on any Unix system where all their dependencies have been installed. Starting with version 4.0.0, Microsoft Windows is also supported, please see the GnomeDB on Windows page for more information about that platform (including compiling instructions).
Binary packages
Linux / Unix
This page does not contain any binary distribution of Gnome-DB. Refer to the packages offered by the Linux distribution to install Gnome-DB (I can add links to externally made binary packages, though).
However some Linux distributions contain already installable packages, which can easily be installed.
Windows
As an exercice, some MS Windows packages have been made available at http://download.gnome.org/binaries/win32/libgda
Some additional information can be found at http://www.gnome.org/~vivien.
Sources
Stable version
The current stable version of libgda is 4.0.6, available at: http://ftp.gnome.org/pub/GNOME/sources/libgda/4.0
Development version
The current development version of libgda is 4.1.4, available at: http://ftp.gnome.org/pub/GNOME/sources/libgda/4.1
Git repository
Libgda is hosted by GNOME's infrastructure, and its git repository is available at: http://git.gnome.org/browse/libgda