Note: See Commons:Categories#Creating a new category for more info. This is the short version.

Summary

1. Put the new category name at the bottom of a file while in edit mode:

[[Category:NEW CATEGORY NAME]]

2. Then click the "Publish page" button. There will now be a red link at the bottom of the file.

3. Click on the red link. This will open an edit window.

4. Add the parent category link:

[[Category:PARENT CATEGORY NAME]]

5. Save the page. You have created a new subcategory.

You can create as many categories, and subcategories, as are needed to correctly categorize image and media files.