Hi mail25,
The best way is to use plugin because while updating to new new version your customized code will not be lost. If you don’t like to use plugin then it needs code customization. We recommended not to change the code because if you change the code then while updating to our new version all your customisation code will be lost. So better make child theme and edit the code.
http://codex.wordpress.org/Child_Themes
Copy all files from header.php and add your code before </head>
tag in child theme header.php. If you are unable to fix it then you need to hire a developer to fix it.
Thank you!