This question is similar to this one and this one, but still different enough to merit it's own Q&A, imho.
As a beginning designer, and up to this day, I have always struggled with a very basic thing in my designs: the feeling that everything is important. This is especially true for flyers, posters, websites and other designs with lots of text.
This is especially true for very basic or non-existent design briefs, where the client/friend/family member expects you to do all the work since 'you're the designer'. Since everything is important, everything needs to be as big and/or colorful as possible, resulting in a crowded, bloated design, where it's really unclear what is actually important.
So, on to the question:
How can a designer create a relationship between equally important content within a design without the design appearing overly cluttered and unorganized?
How can multiple object/items be given "weight" but not overpower each other?
Note: uncluttered is not the same as minimalist or simple. I'm not looking for a way to leave any information off, but rather to decide between what should be seen first, and what should only become apparent on closer inspection.
Note 2: answers with practical examples of posters, flyers, design are much appreciated.