First things first: The Adventures of Tom Sawyer does not, taken together, fit neatly into one of Booker's Seven Basic Plots. Just take a look at the Classic Plot Analysis section to understand why it's so difficult to pin the book down.
That said, it is possible to isolate one particular storyline from within the book that fits rather nicely into the Booker mold, what might be called the story of Huck Finn. The kid's got "Rags to Riches" written all over him.
How's this for wretchedness? Huck Finn's got no mom and no place to live. His dad's known as the town drunk, and he doesn't want anything to do with Huck. None of the other adults in St. Petersburg, Missouri are willing to take him in; they think he's a bad influence on their kids.
Bad or not, Huck does have some influence on the kids: they envy him his independence. As such, he and local troublemaker Tom Sawyer share something of a bond. One day, Huck and Tom get to talking about superstitions, and the two agree to meet in the graveyard at midnight the next day to test out a "cure" for warts.
The meeting turns out to be more important than either Huck or Tom could have ever imagined. The two boys witness Injun Joe murder a local doctor, then frame it on his drunk accomplice Muff Potter. The two boys draw up a contract and promise never to tell a soul about what they've seen. Huck's willingness to commit to the contract represents a step forward for a boy used to having no obligations, and the guilt he feels for not telling the truth and sparing Muff Potter signals a corresponding moral development. At this point, Huck is let off the hook. Tom Sawyer breaks the contract and saves Muff Potter without mentioning Huck's involvement.
After watching Injun Joe and his accomplice take a huge amount of treasure from the "haunted house," the boys decide to follow the criminals and figure out where they've hidden the loot. Once they figure out that Joe hangs out in a strange room in the Temperance Tavern, Huck volunteers to stand watch each night. When he sees two shadowy figures enter the room, then exit very quickly, he follows the two men until they stop just in front of the Widow Douglas's house. When he hears Injun Joe tell the other man that he is going to attack the Widow, Huck has a choice to make: does he run away from the scene in fright or does he help the Widow Douglas?
In the end, Huck sort of does both, by telling the Welshman, an old man living nearby, about what he has just heard. Though the Welshman is not quick to trust Huck, he heads out to the Widow's house anyway. In this case, Huck is able to muster up some courage without the help of Tom Sawyer, and he is rewarded for doing so: the Welshman welcomes him with open arms when he returns the next day. Over breakfast, he tells the Welshman that Injun Joe was the one looking to kill the Widow. Huck, who was once too afraid to say anything regarding the murder, is now able to speak without fear.
Now, Huck finds gets his riches in two ways: 1) he and Tom Sawyer find a big old box of gold coins hidden in the caves, and 2) he is taken in by the Widow Douglas, who gives him a place to sleep, feeds him, and clothes him.
As you can probably tell, Huck's story doesn't fit the rags to riches mold perfectly…and that's before you even consider that Huck doesn't want what the riches bring. Still, it's safe to say that, by the end of the book, Huck is definitely closer to the riches end of the spectrum than he was at the start of the story.