Hi,
if you want to add custom field to the category page (or any category page) you can do so by setting the rule of the field group like that:
[taxonomy terms] [is equal to] [Categories]
you can set the [Categories] drop down to whatever categories you like or you can set it to [All] if you want you custom field group to display on categories AND taxonomies.
then to display the field value on the front end have a look at
http://www.advancedcustomfields.com/resources/functions/get_field/
around * $post_id examples
