It's simple!
From a question: click on the tag you see, and it will bring you to a page of all questions containing that tag. Click on the Star in the upper right corner, and you have favorited it!
From the home page: click on the Tags tab at the top. This will take you to a page of all tags. Click on a tag you like, and it will take you to a page of all questions containing that tag. Click on the Star in the upper right corner, and you have favorited it.
To see your favorites: Click on your user profile. Now click on favorites, and your favorite tags should be listed.
(In some skins, there is a heart instead of a star that you must click to favorite something).