I broke my plugin Options page, please help me fix it

So I have this very simple plugin, which saves a single option using the standard options management functions WordPress offers.
It worked. And while maintaining it, I broke it, only to discover I can’t figure out how it was supposed to work.

The good news: Settings page loads and is populated as expected. I can select an option from the dropdown list and press Save.

The bad news: When the Settings page reloads after save, the old value is restored.
So apparently, I broke the bit that saves the option.

But as I understand it, that’s the bit that happens behind the scenes, based on my correct code.
So apparently, my code isn’t entirely correct, but I can’t figure out where.

I think it all boils down to two things I don’t know/understand:

1. How to the function signatures interact, i.e. what is the $page and the $section I pass to the standard functions?
2. How do I name my form input correctly?

But there may be more I’m not getting, or getting wrong.

Here’s my code:

add_action   ('admin_menu',          'fd_create_settings');
add_action   ('admin_init',          'fd_register_settings' );

function fd_create_settings() {
	add_options_page( 'Vlag van de Dag'
					, 'Vlag van de Dag'
					, 'manage_options'
					, 'fd_settings'
					, 'fd_get_settings_page' );
}
function fd_get_settings_page() {
	echo '<div class="wrap">';
	echo '<h1>Vlag van de Dag-instellingen</h1>';
	echo '<form method="post" action="options.php">';

	settings_fields      ('fd_options');
// Is this correct?                ^

	do_settings_sections ('fd_options');
// Is this correct?                ^

	submit_button();
	echo '</form>';
	echo '</div>';
}
function fd_register_settings() {

		register_setting    	('fd_options', 'fd_current_flag');
// Is this correct?                           ^

		add_settings_section	( 'fd_plugin_main_section'
					, 'Instellingen'
					, 'fd_get_text_section_main'
					, 'fd_options');
// Is this correct?                            ^

		add_settings_field	( 'fd_current_flag'
	 				, 'Huidige vlag'
					, 'fd_get_flags_dropdown'
					, 'fd_options'
					, 'fd_plugin_main_section');
// Is fd_options correct here?                 ^
		}

	function fd_get_text_section_main() {
		echo '<p>Algemene instellingen Vlag van de Dag.</p>';
		}

	function fd_get_flags_dropdown() {

		$flags   = fd_get_flags_array();
		// $flags array is correctly filled with key/value pairs, I've verified
		// So I won't bore you with that code

		$options = get_option('fd_options');
		// $ditto for options array

		$current = $options['fd_current_flag'];
		// $current variable fills correctly with the last saved value

		echo "<select id='fd_current_flag' name='fd_current_flag'>";
		// What I'm nut sure of is if this is correct  ^
		// I thought the name should refer to the option name?

		// Filling the dropdown; the logic to determine the selected option
		// works perfectly, $current gets selected
		$option = '<option value="geen"';
		if($current=='geen') {
			$option .= ' selected';			
			}
		$option .= '>Geen</option>';
		echo $option;
		foreach($flags as $key => $flag):
			$option  = "<option value='$key'";
			if($key==$current) {
				$option .= ' selected';			
				}
			$option .= ">$flag</option>";
			echo $option;
		endforeach;
		echo '</select>';
		}

The page I need help with: [log in to see the link]