Okay, so the query you need is:
SELECT a.name, a.email, n.title, n.submit_time, n.body
FROM news AS n, administrators AS a, categories AS c
WHERE n.category_id = c.category_id
AND c.category_id = 1
AND n.admin_id = a.id
(I assumed that the id field in administrators is called id - you might need to change that).
-Keegan