Humbert loves young girls, which is fine when he is young, but becomes complicated (and illegal) as he gets older.
From the Foreword to Humbert's memoir, we find out that Humbert died in captivity. Soon we begin reading Humbert's story, which begins by describing the childhood love that led him to his obsession with what he describes as "nymphets." A young woman named Annabel Leigh is his first love, but before gratifying his desire for her, Annabel's parents take her away. Humbert's enduring desire for young girls is established in these early chapters. He expresses a range of feelings about it – guilt, desire, rationalization – and explains that, other than nymphets, he only sleeps with prostitutes.
Flash forward to Humbert as a grownup. He moves into the Haze household and meets Lolita, a reincarnation of Annabel.
Humbert falls in love with Lolita, the daughter of his landlady, the mediocre and lowbrow Charlotte Haze. He doesn't stand a chance of getting to Lolita as long as Mrs. Haze is around.
Humbert gets a letter from Charlotte saying basically love me and marry me or get out. He becomes worried that he will be separated from Lolita.
Humbert accepts that in order to continue being around Lolita he will have to bite the bullet and marry Charlotte. Soon after they marry, Charlotte discovers all of Humbert's dirty little secrets, threatens to tell Lolita, but gets killed by a car, freeing up Humbert to pursue Lolita.
Humbert's takes Lolita to a hotel and has his way with her, though he is eager to let us know that she initiated the sexual encounter. (Hmm…)
Humbert finally gets what he has desired for so long. Ironically, before he swoops up Lolita from Camp Q, she has already lost her virginity to Charlie Holmes, with whom she has sex by the aptly named Lake Climax. Being the sex-filled book that it is, Lolita naturally has the climax of the story coincide with Humbert's own sexual gratification. What will Lolita do now that she has given herself to Humbert? As mentioned, one of the shocks of the novel is Humbert's assertion that Lolita seduces him. Once that has happened, we still wonder: Will she leave him? Will she turn him in? They end up going on a year-long trip around the United States and then shacking up in Beardsley.
Someone is on to them.
After being together for several years, things start to go sour between Lolita and Humbert. Lolita gets a role in The Enchanted Hunters, the school play. Lolita and Humbert set off on another trip. This trip is quite different from the last. Humbert's levels of paranoia and jealousy are high. He suspects but cannot confirm that someone is following them and that Lolita is being unfaithful. Finally, as he has feared, Lolita disappears.
After many years apart from Lolita, Humbert tracks her down and finds out that her abductor is none other than the Enchanted Hunters playwright, Clare Quilty.
On a second reading, you can find many clues that indicate Clare Quilty is around and possibly preying on Lolita from early on. It all adds up at the end. Now that Humbert knows who took her, he sets off to kill him.
Humbert murders Clare Quilty.
The long-awaited revenge is enacted. Humbert tracks Quilty down and, after reading him "the charges" in the form of a poem, shoots him several times. No one cares. Humbert goes to jail.