I keep running over in my head just how far in to closure I should get. There is already a tutorial and the Closure: Definitive Guide are great starts. These will be enough to get you up and running for a simple application that runs locally (or on a local server if you went down the plovr route).
Once you have followed the tutorial and got everything setup you'll find your first problem will be XHR. If you are building a site that consumes XHR requests from another domain then running your page off a local server should suffice, the issue comes when you are trying to consume json from your own domain. Since you'll be running your page from localhost (or whatever you're using) you'll run in to cross domain issues.
Building a proxy server in node.js is a bit beyond what this blog is about and it would be terrible of me to take you away from the experience of learning about node.js. Instead I'm just going to let you know the principle and let you go and find your own tutorial.
The idea is that you want to run the server on your localhost, read the requests as it comes in and if it should match something local then read that file and return it. Otherwise you want to copy the headers over to a new request and pipe the response back.
At catch we even decide whether to look at the uncompiled version of the code for development by putting a debug=1 in the query string parameters.