Obviously, David Copperfield is about much more than just David Copperfield. There are a lot of characters whose development follows the classic plot trajectory from initial situation through to conclusion. But David's name is in the title, so we're only going to map his particular quest to a happy, fulfilling family.
As the title of the first chapter announces, "I Am Born." The beginning of the novel starts where any really complete account of someone's life begins, at the main character's birth. David is born to a young widow, Mrs. Copperfield. Already in the first chapter, we can see that David has been born into a fractured family. His father has died and his great-aunt refuses to be his godmother because David is a boy instead of a girl. And his mother is childlike and easily wounded: not a strong parent figure.
David's family life starts out a little precarious, but things don't really get wonky until a dark-haired, handsome, stern gentleman enters his mother's life. This is Mr. Murdstone, and David is the last to know that Mr. Murdstone has designs on David's mother. Imagine the scene: David is sent away to visit his housekeeper's family for two weeks, and when he comes back, his mom's married. And his room isn't even in the same place! Now he lives down the hall from his mother. Mr. Murdstone and his awful sister immediately start scolding David's mother for being too affectionate with her son. They bully and oppress David, and make him feel like he is the worst boy in the world. All in all, his family life is going down the tubes.
But of course, things can always get worse. It's not bad enough that the Murdstones are first verbally and then physically abusive. They send David away to a terrible boarding school, where he is frequently whipped by his headmaster. And then, worst of all, David is away from home when his mother and infant baby brother die. At this point, all ties between David and the Murdstones seem broken. Mr. Murdstone sends his defenseless ten-year old stepson into London to work in his factory. So now, David is about as far from a happy family as he can possibly get: he is an orphan living alone in London, with no future and no prospect for improving his life.
So, David's in a really bad place. He's got nothing to lose, so he risks everything on a last-ditch effort to befriend his great aunt, Miss Betsey Trotwood. David writes to Peggotty, his old nurse, and finds out that Miss Betsey is living in Dover, which is about seventy miles from London. David sets out on the road. After a mishap with a thief, he has to start selling his clothes piece by piece so that he can eat on his way. Finally, he turns up at his aunt's house, and she takes David in. When the Murdstones come to collect David, she sends them away with a few words about what jerks they are. So now, David has a family: a mother figure in Miss Betsey, and a delightful brother figure in her other ward, Mr. Dick.
It looks like David has been given everything he has ever wanted. But we're only a third of the way through the novel, so there must be some future disaster waiting that will prevent David from enjoying his new family. It's not financial disaster, because when Miss Betsey goes broke, David has enough skills and dedication to support her. No, David creates his own obstacle to happiness. His affectionate heart leads him to fall in love with a lady who is completely not right for him, Miss Dora Spenlow. And he's a stubborn, honorable guy, so he marries her and tries to make it work. We know that he's had sparks with Agnes Wickfield since around the time he first met her when he was around 11, but now there's Dora in the way. How will this get resolved?
David realizes that he doesn't want to be married to Dora after he marries her. And he also knows there's nothing he can do about it. He tries to change her, to make her more serious, but it hurts her feelings. So he gives up and resigns himself to being as happy as he can be with the wrong woman. And he's genuinely sad when she starts to get sick and eventually dies.
But – and we hate to say this, because it sounds mean – it's also convenient that Dora dies, because it resolves David's plot line. To find his happy ending, David needs to marry Agnes, and Dora is in the way. Dickens does his best to avoid any appearance of impropriety by sending David to Europe for three years to get over Dora before he moves on with Agnes. Even weirder, Dickens makes Dora ask Agnes to marry David while Dora is on her death bed. So, Dickens is trying to reassure the reader that it's okay that David is kind of happy Dora has died so that he can marry the right woman. Even so, it seems wrong that David's happy family life has to come literally over Dora's dead body.
In David's search for a happy family, the resolution (or denouement, as we like to put it) comes when he marries Agnes, the woman he's meant to be with. The conclusion is everything that happens after that plot resolution: after David and Agnes marry, they set up house and Agnes bears David many children. They name one of their children Betsey Trotwood Copperfield, so Miss Betsey finally gets the goddaughter she was expecting when David was born. All of David's sons like to fly kites with Mr. Dick. And all is right with David's world.