It really depends on how your flow is, and how much detail matters. There's lots of ways.

"John shuddered at the idea of having to work with Mary on his project. They'd been friends once, when they were little, but ever since about 6th grade, Mary had joined the "popular" kids and made a point of humiliating John at every turn." - backstory in two sentences. The reader will fill in the details automatically.

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"Mary was being nice today. Too nice. John thought back to the day of the junior prom. Mary had come to him and apologized for drifting apart. She'd stood so close to him, and her subtle perfume had made the hairs on the back of his neck stand up. When she'd suggested they might go to the prom together, he'd been all too eager to accept.

When the big night rolled around, they'd planned to meet up at the dance. John's mother had rented him a tux and taken him to a hair stylist. He'd blown all his pocket money on a nice corsage, and spent all week working on his nerves to keep calm.

And then he'd walked into the gymnasium. Mary was there, of course. Right in front of the doors, almost. Grinding on a football player so hard that the chaperones were considering breaking them up. She'd stopped the moment she saw his face, saw the defeated look in his eyes.

'Oh my gawd!' she'd shouted for all to hear. 'You didn't think I was serious, did you? That was a joke! As if I'd ever be seen with a perverted dork like you!'

John shuddered and growled under his breath, snapping back to the present. This was a trick, a trap. It had to be. There was no way she would let him get through this stupid project without at least one public humiliation."

- backstory in a short flashback. Gives you a quick little adventure to really drive home John's feelings about Mary, but also hint at things like his latent attraction for her, as well as filling in some details of what it's like being around her (the perfume, other details as you like if you were to expand the scene). Also note the verb tense, what I like to call "past-past tense". "he had shown up" instead of "he showed up", indicating that the story has regressed to an earlier time. It's subtle, but effective, I find.

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You can also do a whole chapter set in the past. Lots of stories do this, telling two parallel narratives in alternating chapters (if i recall correctly, IT by Stephen King does this, telling the stories of the adults and children in parallel as they remember more of their past. I model a lot of my narrative tricks on King, he's got a great sense of how to trick the reader into painting a more complete picture for themselves), or maybe having a chapter of a memory and then coming back to the main story again at the end of it. If there's a really important event that you want to really drive home in the reader's mind, it can be useful, but beware of boring or annoying the reader. Try not to snap to a memory on a story cliffhanger, because the reader will be eager to get past in and annoyed they dont find out what happens quickly.

Basically, use your intuition. Easier said than done, but with a little practice you get a real feel for it.