Sarah,
Your variable $result is actually a handle / pointer to the database results recordset / cursor (depends on the db system you're using).
You done 2 out of the 3 steps that you need to get PHP to display the result data.
Step 1: Build your query (i.e. the $query variable)
Step 2: Send that query to the db and get a handle on where the db has the results (i.e. the $result variable)
Step 3: Fetch the data from the results set (i.e. from where $results is pointing at).
There are a number of possible statements for this, but they all begin mysql_fetch_.
As an example, try adding this line before your echo statement.
$row = mysql_fetch_row($result);
and then changing your echo statement to:
echo "<p>."$row[0]".</p>";
HTH
Justin