Submit form to db

You are serializing your form data before posting it to your PHP function, but you do not unserialize it at the other end. Therefore your check for $_POST['attend'] == 'yes'will always fail.

Try the following (untested).

    function eventAttend() {
    $fields = array( );
    parse_str( $_POST['data'], $fields );
               if($fields['attend'] == 'yes') {

global $wpdb;

                    $wpdb->insert('wp_event_attendants', array( 'event_id' => $fields['event_id'], 'user_id' => $fields['user_id'])); 

                    echo $wpdb->print_error();
                }
     die();
    }