Deeper editing of index.php and single.php

I'd like to fully customize the CSS and html of the main blog page (index.php) and the individual post page (single.php). However, looking in index.php and single.php, I don't see how to get at the actual code, as it's calling php functions I'm not familiar with.

As an example, I'd like to have my index.html page have something like this for the most recent two or three posts:

<div class="post_summary">
<img src="post_image1.png" class="post_image"/>
<h1>Name of first post</h1>
<p class="post_date">December 29th, 2014</p>
<a href="first_post.html">Read more...</a>
</div>

Presumably, this will involve a PHP loop and pulling the featured image, name, and date of each post. Any pointers would be terrific! Thanks for reading.