Use 'tidily' when referring to arranging objects in a careful, organized way. He arranged his desk tidily before starting work.
Pro Tip 2/3
Visual Clarity
'Tidily' often implies that something looks visually pleasing because of its order. The flowers were planted tidily in rows.
Pro Tip 3/3
Positive Impression
Doing things tidily usually gives a positive impression of a person's habits or character. She completed her assignments tidily, impressing her teacher.