Hey,
If you're going to use an application proxy, you do need to have a public app, you can't do this with a private app. I can't give you a pointer to the correct docs really, because there aren't any, really. Which language are you using, by the way? Basically, you set up the application proxy in your partners console. This may or may not filter down to your shop; you may need to uninstall/reinstall your app (I've had issues with this). Once there, it'll forward the request, with the following things in the query string.
path_prefix (the path where this is trying to go), timestamp, signature and shop. You're supposed to use this to verify that the request is coming from the specified shop. You can see how I verify it in the perl api here: http://cpansearch.perl.org/src/ADAMDH/WWW-Shopify-0.993/lib/WWW/Shopify.pm, under calc_proxy_signature, and verify_proxy.
Also, I know this isn't exactly what you're asking, but I've actually just developed an app proxy gift registry/wish list app, which is now in beta, if you'd like to try it out and save yourself the hassle of writing it yourself. Interested?