Can someone help me with this MySQL code?
Seems like you want to inner join the two tables on their Primary Keys.  Does this run for you:

CODE:

SELECT 
    A.ActionID, A.FeedbackID, A.StaffID, A.ActionDate, A.ActionDetails,
    S.StaffName, S.Department

FROM Action AS A
    INNER JOIN Staff AS S ON Action.ActionID = Staff.ActionID