I know that this is an easy task for the most of you, but there are still enough people that are not familiar with Child Themes.
Download the Thematic Theme Framework (current release) from wordpress.org or a stable development release from thematic4you.com and extract the zip file. Take the /thematic/ folder and upload it to your /wp-content/themes/ directory through FTP. Make sure that you upload the whole directory structure of the /thematic/ folder including all subdirectories and files.
Upload the Child Theme
The next step is to find a child theme that is designed to be installed over the parent theme you chose. In this case, I’ll be using our new BT Extended child theme for Thematic. Please be aware, that you need the stable development release of Thematic for this child theme.
Similar to the previous step, you extract the /BTExtended_Thematic/ folder and upload it to the /wp-content/themes/ directory via your FTP client. Make sure that you upload the whole directory structure of the /BTExtended_Thematic/ folder including all subdirectories and files.
Activate the Child Theme
Now that you have both the parent theme and child theme uploaded, the final step is to activate the child theme. In your WordPress admin panel, simply navigate to the Appearance -> Themes menu, and select the child theme you selected. You don’t need to activate the parent theme. All that it needs to do is sit in the theme directory.