You may want to use logging software. You can either buy it or get it online (sometimes you get a free trial). Your child will have absolutely no idea that their every move is being tracked and placed in an invisible file only you can get into and review.
Or you while your child is online you can switch your settings so you can share files and use another computer and literally see everything they are seeing while on your own computer, but they would know you are there, so this is why some parents like logging software.
Kim Komando has some suggestions and an article on it at her site.