Okay, I tried to simplify it a little. Still nothing. Here is what I put together from your advice nad some other help I got:
mysql_query("Update '$views' SET hits=hits+1 WHERE page='$page'"); //update DB to reflect new view
$hits = mysql_query("SELECT hits FROM '$views' WHERE page='$page'"); //retrieve current hits
Still nothing. The code prints "Views: " to the HTML, so obviously the variable is not being assigned a value. I am pretty sure that I need to use that mysql_result function in there somewhere, but I can't figure out how to implement it and I have yet to find something that explains it well enough for me to put it to the correct use. Would it be something like:
$hits = mysql_result('$page',1)