I would like to contribute to open source by enabling a library that builds with GNU's autotools to generate Gobject Introspection files.
A How-To to achieve this is already mentioned on the GObjectIntrospection's wiki page:
Integrate GI in Autotools
GObjectIntrospection/AutotoolsIntegration How to integration your library's build system with gobject-introspection
Unfortunately the link on the wiki page isn't working.
So how can I enable in an autotools project to generate a GIR file from a given header file set?
The wiki is undergoing some reorganization (projects are moving into a Projects/ directory). That page is now at Projects/GObjectIntrospection/AutotoolsIntegration.