Flashbacks

You may remember when Cassy talked about amnesia in literature. But today, I'm going to tell you about when characters do remember things.

Good writers know where to start their story, and it's never the actual beginning.

I think of this quote when I try to decide where to start a story.
If you really started "at the beginning," then you'd be
first inventing the universe. And nobody wants to read all that.

Which means we need to rely on methods other than starting at the beginning to tell us about the things that happened before page one.

Analepsis is the fancy word for flashbacks. If it's an internal analepsis, we're looking back on something that happened earlier within the narrative (something you've already read). External analepsis flashes back to something that happened before the story started (something you didn't get to read about).

There are many ways to present flashbacks. Maybe they'll come as a dream about something horrible in the past, like when Scott Pilgrim dreams about Envy Adams.

from filmscriptwriting.com

Sometimes characters just talk about something that happened in the past. If you're bad at dialogue, you should not attempt this as an exposition tool... people just don't have conversations like, "Hey, remember that thing we did on [date] in [place]?" "Oh, hey, yeah! That was when [person] did [activity] which caused [emotional response]!" Okay, sometimes we do. But it can look awkward on the page.

Side note: Are you guys as stoked about Maze Runner as I am?!?

Or you can get creative with your flashbacks... stories in the fantasy or sci-fi genres can use magic or technology to find ways to bring up memory or dreams or thoughts. You can find a reason to call back a character from the past, and in introducing them to newer characters who didn't know them, you can get a lot of details out. You can use the amnesia tactic that Maze Runner used, and anything leading up to page one has to be explicitly explained to the protagonist (and therefore to the reader).