Get tweets (using the Twitter API 1.1) and cache them using the Wordpress Transient API. You need twitter-api-php (http://github.com/j7mbo/twitter-api-php).

ShowTweets.php

<?php

	function ShowTweets(){
	
		// Setting the name of our transient
		$transName = 'twitter';
		
		// Time that the transient expires (in minutes)
		$cacheTime = 10;
		
		// If the transient doesn't exist, or when the transient has expired
		if(false === ($data = get_transient($transName))){
		
			// Require the Twitter-API-PHP : Simple PHP wrapper for the v1.1 API (http://github.com/j7mbo/twitter-api-php)
			require_once('TwitterAPIExchange.php');
			
			// Set access tokens here - see: https://dev.twitter.com/apps/
			$settings = array(
			
				'oauth_access_token' => "YOUR_OAUTH_ACCESS_TOKEN",
				'oauth_access_token_secret' => "YOUR_OAUTH_ACCESS_TOKEN_SECRET",
				'consumer_key' => "YOUR_CONSUMER_KEY",
				'consumer_secret' => "YOUR_CONSUMER_SECRET"
			
			);
			
			// Set the url for the Twitter search
			$url = 'https://api.twitter.com/1.1/search/tweets.json';
			
			// Pass all the search parameters (https://dev.twitter.com/docs/api/1.1/get/search/tweets)
			$getfield = '?q=%23dv2013';
			$requestMethod = 'GET';
		
			// Now we get the tweets from Twitter-API-PHP
			$twitter = new TwitterAPIExchange($settings);
			
			// We get the JSON data from the requested tweets
			$data = $twitter->setGetfield($getfield)->buildOauth($url, $requestMethod)->performRequest();    
			
			// We decode the JSON to get a PHP array
			$data = json_decode($data, TRUE);
		
			// We store the data in a transient
		    	set_transient($transName, $data, 60 * $cacheTime);
		    
		}
		
		// We get the tweets from the stored transient
		$data = get_transient($transName);
		
		// We get the statuses array (containing all the tweets from the search we are performing)
		$data = $data['statuses'];
			
		// Check we have any tweets
		if(is_array($data)) {
		     
		    // If we have tweets, we print the container of the tweets
		    print('<div class="slides_container">');
		     
		    // Get the first 5 tweets
		    array_splice($data, 5);
		     
		    // For each tweet
		    foreach($data as $tweet) {
		    
		    	// The user data is in a nested array, so here we define it
		        $user = $tweet['user'];
		        
		        // Print the tweet (change the markup to your liking)
		        print('<div class="slide"><p><a href="https://twitter.com/' .$user['screen_name']. '" target="_blank">@' .$user['name']. '</a> '  . HandleLinks($tweet['text']) . '</p></div>');
		        
		    }
		     
		    // If we have tweets, we print the closing tag of the container of the tweets
		    print('</div>');
		}
	
	}
	
	// Function to create links in the tweet's text
	function HandleLinks($v) {
	    
		// Creating links for URL's
		$v = preg_replace('@(https?://([-\w\.]+)+(/([\w/_\.]*(\?\S+)?(#\S+)?)?)?)@','<a href="$1" target="_blank">$1</a>', $v);
		// Creating links for usernames
		$v = preg_replace('/@(\w+)/','<a href="http://twitter.com/$1" target="_blank">@$1</a>',$v);
		// Creating links for hashtags
		$v = preg_replace('/\s+#(\w+)/',' <a href="https://twitter.com/search?q=%23$1" target="_blank">#$1</a>', $v);
		
		return trim($v);
	     
	}
	
	// Usage:
	ShowTweets();

?>

I'm a little lost ...

Where should I enter the username?