Just to be sure, do I copy the header.php file that’s presently in my Twenty Ten theme, put the Google Analytics code in the copy, and upload the file into my child theme? Also, I presently have a Google Plus script code in my footer.php file. Should I do the same with the footer.php file, copy and upload to the child theme? Thanks for advice.
If you’re using Twenty Ten, there’s no reason to edit the theme for these things. You can use the wp_head and wp_footer actions to output the relevant scripts.
That said, if you prefer to edit the theme, then modifying header.php and footer.php in a child theme is the right approach. Though it’s unlikely that Twenty Ten will be updated, it’s safest to make your changes in a child theme.
Thank you for this information, Krishna and Erick!