The simplest way to use WordPress feed from non-WordPress sites is relying on a library: SimplePie that is the same used by WordPress itself.
You can download it from its site, there is also a minified version.
Normally you download it as zip package, extract it in a folder, name it simplepie, and put in your non-WordPress in the same folder of the file that should output the feed.
After that using it is very easy, in the file where you want to output feed just do something like:
<?php
// following lines go before open html tag
require_once 'simplepie/autoloader.php';
$feed = new SimplePie();
$feed->set_feed_url( 'http://blog.example.com/feed/' );
$success = $feed->init();
$feed->handle_content_type();
?>
<html lang="en-US">
<head>
<title>SimplePie Demo</title>
<link rel="stylesheet" href="https://wordpress.stackexchange.com/questions/136904/yourstylesheet.css" type="text/css" media="screen">
</head>
<body>
<?php
if ($success) {
foreach( $feed->get_items() as $item ) {
echo '<h4><a href="' . $item->get_permalink() . '">';
echo $item->get_title() .'</a></h4>';
echo '<p>' . $item->get_date('j M Y, g:i a') . '</p>';
echo '<p>' . $item->get_content() . '</p>';
}
} else {
echo 'Error on parsing feed';
}
?>
</body>
</html>
Of course feel free to customize the markup, the mine is just a quick rough example.
Consider that SimplePie has powerful functions to handle categories and tags, images and other media, cache, sanitization and much more.
See documentation and API docs and also have a look at the demo folder in SimplePie package, it contains useful examples.