Authenticate Users on web-app through moodle

I am developing a mobile web-app using jQuery and HTML5 which I am going to deploy onto iOS and android app stores using PhoneGap.

This app needs users to Login using a Moodle username and password, before it can let them use the app.

I have absolutely no idea how to do this.

So here's my question. How do I take a user's Username and password, send it to Moodle to authenticate and handle the response?