In order to add fields to a Media Type, go to Settings and then Media Types & Fields.
Choose the desired Media Type in the drop-down menu, select the desired field to add in the right-hand sidebar. You can filter the available options by typing the name of the field in the upper right-hand corner or scroll through the list. Choose between an entry or a header field.
Simply hit + on the right side of each column name or click on the field to highlight it, then drag and drop it into the desired place onto the sheet view.
The field order can be adjusted by dragging and dropping the fields to the desired position.
Always remember to hit Save changes whenever you make updates to a Media Type.