just add your button in after echo $row['Price']; but before the closing }
you could use a graphic button, a form or text. for example.
$result = mysql_query("SELECT * FROM Products");
while($row = mysql_fetch_array($result))
echo '<a href="add_to_cart.php">Add to Cart</a>';
you would need to add in the id of the product so the add_to_cart page knows which product you have selected.