All You Need to Know about Categories in WordPress
Start right away with the habit to create categories and place your post in the appropriate category.
How to make categories visible on your post
Click on top of the post on screen options, check the box before categories
How to add the category widget to your site bar?
How to customize your categories?
Go to customize site and choose for:
Display as Drop down
Show post counts
You can give the category widget a title, but that is optional.
Add Categories to pages
For that matter you need a plugin (Thanks Trish!)