How to assign categories to a page

The answer? You can't!

It's a common misconception that in order to add a category page to your navigation menu, you need to create a "regular page" for it. This is incorrect. Category pages are automatically created when you create a category. Your blog posts cannot be "assigned" to display on a certain page that you create; your categories have their own automatic pages. The category pages are not found in your WordPress dashboard under Pages, but are instead found at Posts > Categories.

For example, if you want to have a category called "Travel" on your site, do not create a page called Travel. Instead, create a category called Travel. Then, to use that category in your navigation menu, follow the instructions here.