I made a .capx that should show how to use some of the Gamejolt API functions in construct 2. It was made in the latest beta release of construct 2 (123.2)
You will need Kyatric's CBHash plugin, which is here
Basically, you just use the ajax object to send the api calls to the gamejolt servers, and use the CBHash plugin to provide the signature to verify the calls.
So far I've only really used the api to award trophies, so that's all that this capx shows, but once you have the basics all the api functions are accessed in pretty much the same manner. There's a list of them at gamejolt.com/api/doc/game
Hopefully the .capx is pretty straight forward, but If I'm being confusing let me know and I will attempt to clarify.