Login to the site and you'll see a black menu at the top with a lot of options on it (I've expanded your access at the back end of the site but most of it you can completely ignore).

Click on "Content" and a list of all the items on the site will be displayed. You can scroll through the list, or use the search box at the top to filter the list to find the item you want to change. Click on edit out to the right to edit the piece and you'll see the Category option which will display any that are set under the Category Heading > All Sections, or you can use the box under category to select. Use Remove to delete any incorrect categories. 

When you select a category using the drop down box - as per the note on the screen:

Make sure you click "Add" after choosing your categories as they must be saved first and displayed to be saved when the page is saved.