Using Taxonomy an Vocabulary allows you create the categories for your Drupal Blog. Let me make it easy by this
1 : Setup Vocabulary in Taxonomy
The first thing you need to create Taxonomy unser Structure link
And now you need to add Vocabulary and Term
You can readmore at "Create Content Type and Term in Drupal"
2 : Add Field in Content Type
Select manage fields
Create new field and enter name for Contrent Type.
Make Field Type "Term Reference" and choose which taxonomy applies.
On the next screen choose Save field settings
and next choose Save settings
3 : Create new post and now you can set category.