In simple terms, why are scientists so convinced that most of the universe is made up of dark matter and dark energy?

When I first heard this, it seemed as if the data were being fudged. Since the data do not agree with the theory, we will just have to create new data.

I can understand that observations require more matter and energy than we can account for, but why must it be something completely different from ordinary matter and energy? What makes us so sure that we can account for all of the ordinary matter and energy? And what does it mean when they say that dark energy makes up 72% of the universe? How do you compare matter and energy? The only way that I know of would be to apply the formula E=mc^2 to matter. That would be an awful lot of energy.

Where is this dark matter and energy supposed to be lurking? Is there any of it in our galaxy, in our solar system? It all seems really bizarre and in need of an explanation understandable by the common person.