There are a few different ways for categories to show up on your site once you've created them.
1. Create a new Menu called "Category Menu" and assign it to one of the available menu locations.
This can be done by going to Appearance > Menus (Or with the Customizer located under Appearance > Customize > Menus)
To create the menu select Create Menu, name it, and save it.
Once you've saved the menu, on the left select the Categories option.
Check off the categories you want to show and select Add To Menu. (Don't forget to Save your changes)
Depending on your theme, you will be able to assign the menu to a Primary or Secondary location from the tab at the top called Manage Locations (not all themes support this).
When you create a new category is does not get automatically added to your menu. You will need to manually add new categories to your menu if you add them later.
2. Drag the Categories widget to any available widget are to show a list of categories.
You can find this widget and the available widget areas for your theme under Appearance->Widgets (Or in the Customizer under Appearance > Customize > Widgets)
NOTE: Categories in WordPress will only be displayed in this widget if there are posts assigned to that category. If a category has been created, but no posts have been assigned, it will not be displayed in the category listing. Once you've added a post to the category it will start showing.
3. You may also use the Custom Menu widget to display the categories a little differently in one of the available widget areas.
The list will look a little more like a navigation menu rather than a simple list of categories.