To add new vocabularies, using the add vocabulary tab at the top of the page. Or go to: admin/ content/taxonomy/addvocabulary.

Step 1: Choose a name for your vocabulary, for example, Blog category.

Step 2: Add a description.

Step 3: Choose content type: "story", "book page" or whatever. In this case, because you want to have categories on Blog, they should be “Story”. Then when users create content of a particular type, they'll see a list of your vocabulary terms that go with it.

Step 4: If you allow "free tagging", when your users create content they can make up their own terms as they go along, instead of having to choose from a list.

Step 5: By choosing "multiple select", this allow your users to put a post into more than one category at once by tagging it with more than one vocabulary term.

Step 6: Require option is that when your users create content of a certain "content type" they assign at least one of this vocabulary's terms.

Step 7: You can add "weight" to it to specify the order of appearance.

Step 8: Finally click on save.

This is screenshot:

Master Drupal in 7 hours - Advanced Customization - Create category - Creating a vocabulary