Taxonomy is one of the Drupal Core Modules. Before you can apply categories and tags on node. You have to define them @ Administer –>> Content management –> Taxonomy.

In this example, i would like to specific some Tags for Stories node type. So i create a Vocabulary called Stories. You can allow user to enter his/her own Terms/Tags or multiple selection in the Settings tab.

 

Then i created a few Terms in the Stories Vocabulary.

 

You can now edit the Story node type and pick some tags for them.

 

Done =)

Reference: Organizing content with taxonomy