How to prevent multiple form submission on multiple clicks in PHP

Use a unique token generated each time you display a form and which can be used only one time; it is also usefull to prevent CSRF and replay attacks.
A little example :

<?php
session_start();

/**
 * Creates a token usable in a form
 * @return string
 */
function getToken(){
  $token = sha1(mt_rand());
  if(!isset($_SESSION['tokens'])){
    $_SESSION['tokens'] = array($token => 1);
  }
  else{
    $_SESSION['tokens'][$token] = 1;
  }
  return $token;
}

/**
 * Check if a token is valid. Removes it from the valid tokens list
 * @param string $token The token
 * @return bool
 */
function isTokenValid($token){
  if(!empty($_SESSION['tokens'][$token])){
    unset($_SESSION['tokens'][$token]);
    return true;
  }
  return false;
}

// Check if a form has been sent
$postedToken = filter_input(INPUT_POST, 'token');
if(!empty($postedToken)){
  if(isTokenValid($postedToken)){
    // Process form
  }
  else{
    // Do something about the error
  }
}

// Get a token for the form we're displaying
$token = getToken();
?>
<form method="post">
  <fieldset>
    <input type="hidden" name="token" value="<?php echo $token;?>"/>
    <!-- Add form content -->
  </fieldset>
</form>

Combine it with a redirect so you keep a perfect backward and forward behavior.
See the POST / redirect / GET pattern for more information about the redirect.