Welcome to the world of PHP.
The mysql -extension is outdated perhaps consider using Mysqli or PDO.
Other than that, one of your problems will be here:
$select_posts = "select * from posts order by rand() LIMIT 0,2";
$run_posts = mysql_query($select_post);
Where you use $select_posts and then $select_post, probably a typo but it'll stop the SQL from being run.. Same thing applies to $run_posts and then $run_post. So double check all your variable names to make sure you have them right.
As a tip, when you're constructing your SQL try to capitalise keywords for better readability, i.e.
$select_posts = "SELECT * FROM posts ORDER BY RAND() LIMIT 0,2";
Edit: Try this:
<?
include("includes/connect.php");
$select_posts = "SELECT * FROM posts ORDER BY RAND() LIMIT 0,2";
$run_posts = mysql_query($select_posts);
while($row=mysql_fetch_array($run_posts)) {
$title = $row['post_title'];
$date = $row['post_date'];
$author = $row['post_author'];
$image = $row['post_image'];
$content = substr($row['post_content'],0,200);
}
?>
<h2><?php echo $title; ?></h2>