I'm working on an application that relies on data that the browser sends within the HTTP headers (and there's no way around this). This also happens to be my first time working with something node.js based, so it's very likely I'm completely missing something simple!
Basically what I want to be able to do is call a method on the server from the client, and in that method read the HTTP headers that the client sent.
Meteor doesn't yet provide a supported API for serving HTTP from your app. This is intentional: in the not-too-distant future, your app server is likely to not be just a single process directly serving end users, but an arbitrarily parallelizable service behind a proxy tier. So we'll need to provide a supported API for responded to HTTP requests (REST, eg) that continues to work in such a setting.
Are you sure it needs to be HTTP and that you can't just use a Meteor method?
If you really need to accept direct HTTP requests now, take a peek at how packages/accounts-oauth-helper/oauth_server.js uses __meteor_bootstrap__.app to hook into the Connect middleware framework. This will work for now, but we don't promise that Meteor will always be powered by Connect :)