You need to ‘show’ your reader information, not simply ‘tell’ them. This way you ‘expose’ the back story without being boring. And some of the best ways to do this are through dialogue, conflict, revealing a character’s thoughts and using physical props such as newspapers, letters and emails.
For example, have your characters talk to each other about events that have happened, what those events meant to them, how they felt and reacted to those events. But a word of warning. You need your dialogue to be realistic. Don’t use it as a way of dumping information. And make sure your characters never tell each other things they already know.