settings.php

<?php
/**
 * Plugin Name: My Plugin
 * Plugin Description: Settings API Demo
 * Text Domain: my-plugin
 */

add_action( 'admin_menu', 'my_admin_menu' );

function my_admin_menu() {
	add_options_page(
		__( 'My Plugin', 'my-plugin' ), // $page_title
		__( 'My Plugin', 'my-plugin' ), // $menu_title
		'manage_options', // $capability
		'my-plugin', // $menu_slug
		'my_options_page' // $function
	);
}

function my_options_page() {
	?>
	<div class="wrap">
		<?php screen_icon(); ?>
		<h2><?php _e( 'My Plugin Options', 'my-plugin' ) ?></h2>
		<form action="options.php" method="POST">
			<?php settings_fields( 'my-settings-group' ); /* $option_group */ ?>
			<?php do_settings_sections( 'my-plugin' ); /* $page */ ?>
			<?php submit_button(); ?>
		</form>
	</div>
	<?php
}

add_action( 'admin_init', 'my_admin_init' );

function my_admin_init() {

	// Sections
	add_settings_section(
		'section-one', // $section_id
		__( 'Section One', 'my-plugin' ), // $title
		'section_one_callback', // $callback
		'my-plugin' // $page
	);

	// Fields
	add_settings_field(
		'field-one', // $field_id
		__( 'Field One', 'my-plugin' ), // $title
		'field_one_callback', // $callback
		'my-plugin', // $page
		'section-one', // $section_id
		array()
	);

	// Settings
	register_setting( 
		'my-settings-group', // $option_group
		'my-setting', // $option_name
		'esc_attr' // $sanitize_callback
	);
}

function section_one_callback() {
	_e( 'Some help text goes here.', 'my-plugin' );
}

function field_one_callback() {
	$setting_value = get_option( 'my-setting' ); // $option = $option_name
	echo '<input class="regular-text" type="text" name="my-setting" value="' . esc_attr( $setting_value ) . '" />';
}