Download Composer
In your project directory run:
php composer.phar require sunra/php-simple-html-dom-parser ~1.5
In your php file (index.php for example), add:
<?php
include 'vendor/autoload.php';
use Sunra\PhpSimple\HtmlDomParser;
$dom = HtmlDomParser::file_get_html();
Here, when you include vendor/autoload.php
the composer generated autoloading configuration handles all class autoloads for you. Nearly all libraries on github that follow PSR-0 exist on Packagist making them available for install in this way.
You may want to read up on Semantic Versioning to get an idea of what you are installing when you require libraries.
Most modern PHP frameworks now use Composer for their dependencies. However it is still fully feasible for small projects of even a single file.