Making a child theme is very simple. Create a directory by using FTP or whatever file management application your host provides. Put a properly formatted style.css file in it, and you have a child theme!
The child theme contains a “Template: parent-theme-dir” header to distinguish it from standalone themes. With a little understanding of HTML and CSS, you can make that very basic child theme modify the styling and layout of a parent theme to any extent without editing the files of the parent theme itself. That way, when the parent theme is updated, your modifications are preserved.
For this reason, child themes are the recommended way of making modifications to a theme.
With a basic understanding of PHP, WordPress Templates, and the WordPress Plugin API, you can make the child theme extend virtually every aspect of a parent theme, and again, without actually changing the parent theme files.
A child theme resides in its own directory in wp-content/themes. The scheme below shows the location of a child theme along with its parent theme (Twenty Twelve) in a typical WordPress directory structure: