Wordpress - 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
}

To modify the header in a child theme, copy the header.php from the parent theme into the child theme and then modify it. WordPress will see that you have a header.php in your child theme and use that instead of the parent theme header.php

Any template files you put in your child theme will take priority over the same file in the parent theme when called by WordPress.

Anything that goes in the tag should be done using something such as the function in Brians answer. If it's theme specific, you can put it in a file called functions.php in your theme folder without any extra steps.

Thanks to Brian Fegter. If this answer helps, please rate for Brian's answer right here above.

This is a fully functional example of how to add things to the "header" by its own plugin. In this case, I am adding the properties of Facebook Open Graph for the Share and Like buttons.

Just create a PHP file with the name specified in "Plugin Script" at the beginning of the sample code, place it in a folder with the same name without the extension, obviously, and copy this folder to the destination "/ wp-content / plugins".

Then within "Wordpress", refresh "Plugins" and you'll see your new plugin installed. Just Activate it, and your pages will begin to contain the metadata of Open Graph Facebook and Twitter.

VERY IMPORTANT: The PHP file must be encoded in UTF-8 without BOM, and should have absolutely no character at the end. Must ensure this.

<?php
/*
    Plugin Name: My Facebook Open Graph Protocol
    Plugin Script: my-facebook-open-graph-protocol.php
    Plugin URI: 
    Description: Add Facebook Open Graph Protocol to header
    Author: Diego Soto (Thanks to Brian Fegter)
    Donate Link: 
    License: GPL    
    Version: 0.1-alpha
    Author URI: https://wordpress.stackexchange.com/questions/43672/how-to-add-code-to-header-php-in-a-child-theme
    Text Domain: myfogp
    Domain Path: languages/
*/

/*  Copyright 2014 Diego Soto  (http://disientoconusted.blogspot.com.ar/)

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License, version 2, as
    published by the Free Software Foundation.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
*/

add_action('wp_head', 'wpse_43672_wp_head');

function wpse_43672_wp_head(){
    $title = get_the_title() ." &lsaquo; ". get_bloginfo( "name", "display" );

    $src = wp_get_attachment_image_src( get_post_thumbnail_id(get_the_ID()), array( 90,55 ), false, "" ); 

    $face_metad = get_post_meta(get_the_ID(), "metadescription", true);

    $twitter_metad = get_post_meta(get_the_ID(), "metadescription140", true);
    if (empty($twitter_metad)) 
        $twitter_metad = $face_metad;

    //Close PHP tags 
    ?>    
    <meta property="og:title" content="<?php echo esc_attr($title); ?>" />
    <meta property="og:image" content="<?php echo esc_attr($src[0]); ?>" />
    <meta property="og:url" content="<?php the_permalink(); ?>" />
    <meta property="og:description" content="<?php if (!empty($face_metad)) echo esc_attr($face_metad); else the_excerpt(); ?>" />

    <meta name="twitter:title" content="<?php echo esc_attr($title); ?>" />
    <meta name="twitter:image" content="<?php echo esc_attr($src[0]); ?>" />    
    <meta name="twitter:url" content="<?php the_permalink(); ?>" />
    <meta name="twitter:description" content="<?php if (!empty($twitter_metad)) echo esc_attr($twitter_metad); else the_excerpt(); ?>" />
    <?php //Open PHP tags
}
?>

Anyone who is interested in the functionality of the plugin.

• The title will be the concatenation of the name of the current page and the site name.

• If a custom field called "metadescription" exists, the plugin tries to take the description from this field. Otherwise, take the description from the excerpt.

• As the image, the plugin tries to use the thumbnail of the featured image on the page.