The によると can be other sources: for example, a newspaper, tv, a weather report, the radio, an ad flyer. 'According to' is a very good way to think of it. You are restating information/report that you got from that source.
のうえで can also mean this and function in the same way. However, it can *also* refer to a standpoint from which to consider something.
授業のうえで < As far as class is concerned (Considering class...)
So I'd say that によると is the same as *one* of the meanings of のうえで.
