One of the approaches that you can use to achieve what you require is by using a database to store the available spots and update accordingly.
You can create a database table just for the spots available. 
Make the html signup code a submit rather than a class (if you want to use php only) or you can use javascript or jQuery to act as submit if clicked (onclick), you can find a topic/tutorial here: Click Here
then a code like:
if(isset($_POST['name_of_submit_button'])) {
    // Set query to update accordingly
    $query = "UPDATE available_spots_table
          SET available_spot = available_spot - 1
          WHERE id = 1"; // You can use ID to identify the 
    // Run the query
    $run_query = mysql_query($query);
    // Some other code here
 }
And you can show it by pulling the data from a database like mysql and using php or even javascript if required.
//PHP:
$remaining_spots = '';
$query = "SELECT available_spots FROM available_spots_table WHERE id = 1"; // Select the number of available spots
// Run the query
$run_query = mysql_query($query);
if(@mysql_num_rows($run_query) > 0){  // If query is succesful
  $result = mysql_fetch_array($run_query);  // Get results
  $remaining_spots = $result['available_spots'];  // Assign result into the variable that you will use to display
} else {
   // return fail message
}
$spots_remaining
//HTML : 
<p><?php $remaining_spots ?> spots remaining at Current Price.</p>
This code sample is just to demonstrate how it can be achieved. However, there are other things to consider like : when a user clicks the signup, you might want to setup a code that verifies that the user did sign up before you update the available_spots_record. Also, because php processes the whole page before being displayed, you have to use javascript/jQuery to show it in real-time. The process is also demonstrated using the procedural mysql, you might wanna consider something like an object oriented php/mysqli or use mysqli = LINK. Lastly, you can also create functions to make this process easier.
Thanks.