Webservice
The sourcecode of the webservice gpodder.net is released as open source under the AGPLv3 and hosted at GitHub. Bugs can be reported at the gPodder Issue Tracker on GitHub.
Integrating Clients
If you want to integrate gpodder.net in some podcasting client, you might want to use one of the existing client libraries.
There are already several clients for different platforms which can be used as examples. See list of clients.