Basically, if you do not want to create your own network admin settings page, you will need to use both hooks mentioned separately in the other two answers:

add_filter( 'wpmu_options' , 'show_my_network_settings' );
add_action( 'update_wpmu_options', 'save_my_network_settings' );

function save_network_settings() {
  // checkbox example
  if( isset( $_POST['my_network_checkbox'] ) )
    update_site_option( 'my_network_checkbox', '1' );
 
  // textfield example
  if( isset( $_POST['my_network_textfield'] ) )
    update_site_option( 'my_network_textfield', sanitize_text_field($_POST['my_network_textfield']) );
}

function show_network_settings() {
    $checkbox = get_site_option('my_checkbox'); 
    $text = get_site_option('my_text'); 
    ?>
    <h3><?php _e('My Network Settings','my-plugin'); ?></h3>
    <table class="form-table">
        <tbody>
            <tr>
                <th scope="row"><?php _e('My Checkbox','my-plugin'); ?></th>
                <td>
                    <label>
                        <input type='checkbox' name='my_checkbox' value='1' <?php checked( $checkbox, '1' ); ?> /> 
                    <?php _e('Check my box.','my-plugin'); ?>
                    </label>
                </td>
            </tr>
            <tr>
                <th scope="row"><label for="my_text"><?php _e('My Text','my-plugin'); ?></label></th>
                <td>
                        <input type='text' name='my_text' value='<?php echo $text; ?>' />
                </td>
            </tr>
        </tbody>
    </table>
    <?php
}

For a very clear explanation and useful code sample see http://zao.is/2013/07/adding-settings-to-network-settings-for-wordpress-multisite/

Basically, if you do not want to create your own network admin settings page, you will need to use both hooks mentioned separately in the other two answers:

add_filter( 'wpmu_options' , 'show_network_settings' );
add_action( 'update_wpmu_options', 'save_network_settings' );

function save_network_settings() {
  // checkbox example
  if( isset( $_POST['my_network_checkbox'] ) )
    update_site_option( 'my_network_checkbox', '1' );
 
  // textfield example
  if( isset( $_POST['my_network_textfield'] ) )
    update_site_option( 'my_network_textfield', sanitize_text_field($_POST['my_network_textfield']) );
}

function show_network_settings() {
    $checkbox = get_site_option('my_checkbox'); 
    $text = get_site_option('my_text'); 
    ?>
    <h3><?php _e('My Network Settings','my-plugin'); ?></h3>
    <table class="form-table">
        <tbody>
            <tr>
                <th scope="row"><?php _e('My Checkbox','my-plugin'); ?></th>
                <td>
                    <label>
                        <input type='checkbox' name='my_checkbox' value='1' <?php checked( $checkbox, '1' ); ?> /> 
                    <?php _e('Check my box.','my-plugin'); ?>
                    </label>
                </td>
            </tr>
            <tr>
                <th scope="row"><label for="my_text"><?php _e('My Text','my-plugin'); ?></label></th>
                <td>
                        <input type='text' name='my_text' value='<?php echo $text; ?>' />
                </td>
            </tr>
        </tbody>
    </table>
    <?php
}

For a very clear explanation and useful code sample see http://zao.is/2013/07/adding-settings-to-network-settings-for-wordpress-multisite/