Origin West is our first theme to include the user’s Instagram feed. In order to access the user’s feed they will first have to authorize your application (in this case, a theme). Check out the Instagram developer site for their oAuth details.
I have seen a few themes put together a Tumblr static page to send the authorization request as well as return the access token, but we simply put together a quick page at stylehatch.co/instagram.
We’re working on setting up the Style Hatch Github account where we are planning our process as well as a few other jQuery plugins that we use, like our resizable custom photoset grid.