Cannot get Twitter API 1.1 to work

I have been using the Twitter API code below to list some Twitter feeds on a website. Unfortunately Twitter has made some changes which require you to autenticate yourself before you can use the script.

I understand you have to use oAuth to authenticate access to the API.
https://dev.twitter.com/docs/auth/oauth

Unfortunately I cannot understand how to integrate this into the script. Or is this something that has to be done separately?

JQTWEET = {
	
	// Set twitter username, number of tweets & id/class to append tweets
	user: 'twitterscreenname',
	numTweets: 2,
	appendTo: '#jstwitter',

	// core function of jqtweet
	loadTweets: function() {
		$.ajax({
			url: 'https://api.twitter.com/1.1/statuses/user_timeline.json',
			type: 'GET',
			dataType: 'jsonp',
			data: {
				screen_name: JQTWEET.user,
				include_rts: true,
				count: JQTWEET.numTweets,
				include_entities: true
			},
			success: function(data, textStatus, xhr) {

			 var html = '<div class="tweet">TWEET_TEXT';

				 // append tweets into page
				 for (var i = 0; i < data.length; i++) {
					$(JQTWEET.appendTo).append(
						html.replace('TWEET_TEXT', JQTWEET.ify.clean(data[i].text))
							.replace(/USER/g, data[i].user.screen_name)
							.replace('AGO', JQTWEET.timeAgo(data[i].created_at))
							.replace(/ID/g, data[i].id_str)
					);

				 }					
			}	

		});
		
	}, 
	
		
	/**
      * relative time calculator FROM TWITTER
      * @param {string} twitter date string returned from Twitter API
      * @return {string} relative time like "2 minutes ago"
      */
    timeAgo: function(dateString) {

	}, // timeAgo()
    
	
    /**
      * The Twitalinkahashifyer!
      * http://www.dustindiaz.com/basement/ify.html
      * Eg:
      * ify.clean('your tweet text');
      */
    ify:  {

    } // ify

	
};

$(document).ready(function () {
	// start jqtweet!
	JQTWEET.loadTweets();
});

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