How to add code to Header.php in a child theme?

I would hook into the wp_head action. I would place this in a plugin so as to abstract it from your presentation layer. This allows for scalability and changing of themes. This also prevents any analytics collateral damage if a step is missed in migration from one theme to the next.

add_action('wp_head', 'wpse_43672_wp_head');
function wpse_43672_wp_head(){
    //Close PHP tags 
    ?>
    ADD YOUR PLAIN HTML CODE HERE
    <?php //Open PHP tags
}