What I want to do is use the built in search engine I currently have running in my Drupal site, but allow another site to use that same search engine. Basically a legit copy and paste of the form code.
The reason being is I have a separate web application that is running and I am copying the exact look and feel of the Drupal site to make it seem as if the web application is part of the web site. It's separate because the functionality would be a pain to implement in Drupal, and I could do it in Rails in 30 minutes.
So, what things do I need to configure in Drupal and in my web application to make this happen?
EDIT: Just to clarify, my external web application is not consuming any data from Drupal what-so-ever. All I want to do is POST the "copied" search form to the Drupal engine and have it render the search results as if you had searched directly from the Drupal site. It seems like the Services module is used to streamline data to external web applications, and that is not the workflow here at all.
EXAMPLE: Say I have my Rails application sitting at http://app.hostname.com/ and my Drupal site sitting at http://hostname.com/. There is a search form at the root of my Rails application that is pretty much a copy paste of the browser code you'd see as if you had looked at the Drupal site source of the search form. It's just a simple text box with a submit button. When I submit that form from the Rails site, I want it to POST the data to the Drupal site and have the returned results be the exact same as if I had searched from the Drupal site directly (I said this already but it doesn't hurt to re-iterate), leaving the URL bar now saying http://hostname.com/search/node/foo%20bar.