I want a quarter!
There are different types of breakups, and they are approached in different ways.
There's the slow breakup, where they just start drifting apart. They start doing different things, and mixing with others as individuals, rather than as a couple. Eventually, they find they just aren't spending time with each other and they'll either fix that, or acknowledge it and separate (or maybe one will try to fix it and the other will try to acknowledge it....). From a writing point of view, you can introduce this one early -- having each character do different activities, and then have those activities start to take more and more of their time:
"Joe, how about we go see a movie on Saturday night?"
"Sorry, Rick, but I've got to help set up the stage for the drama club's play."
"You've been working with them for the last three Saturdays. When are you going to spend time with
me
?
"Hey, I know we haven't been going out much recently, but it's a big thing for them. They're depending on me!"
There's the traumatic breakup, where something happens to tear them apart. Usually, it'll involve one person break trust, or appearing to break trust. If you want them back together, you have to make sure that it's all a big misundertanding, but a lack of communication stops them from working that out.
Then there are lots of variations in between. The couple that starts to drift apart, and then a misunderstanding occurs that rips them apart.