Add to the bottom of the page content the following:
[[Category: Your Category Here]]
Replace the words "Your Category Here" with your own category. Type the rest exactly as you see it. You can add multiple categories. They will be listed in the order in which you type them. For instance:
[[Category: Your First Category Here]]
[[Category: Your Second Category Here]]
[[Category: Your Third Category Here]]
2) To add make any category into a subcategory...
First open the category page. The page you open should be the page for the intended child category, not for the intended parent category. You can open any category page by first visiting your Special Pages link in your Toolbox. Then visit the Categories link. Then click on the category that you wish to make into a subcategory. Open the page in edit mode and then add a category tag. Whichever category is specified in the category tag will become the parent category. The syntax is the same:
[[Category: Your Parent Category Here]]
3) To feature a category tree in your MediaWiki wiki...
You will need to install the CategoryTree extension, which you can find at the following link (until the page is moved):