The theme uses modules to display posts and each module can display the post category tag. In the following image you can see how the tags look on a module on the front-end:
Multiple categories case:
If the post is included in more than one category the first one will be displayed. If you want to show a specific category, you have to set a primary category from the post editing section.
How to enable the category tag?
Using the Flex blocks/ Flex grids, you can set the category tag directly in the block settings.
For the default theme blocks to enable or disable the category label, use the switches included in Theme Panel > Block Settings > Category tag on Modules/Blocks