You can read a more detailed plot summary in my link below. Enotes is excellent for that. So instead of summarizing I will discuss, as you ask in your question.
First of all, the storyline is pretty complicated. There are a lot of characters, and the book is full of action. Little Oliver starts out as an orphan in a workhouse, but he eventually gets sent to work for a coffin-maker after famously asking for more gruel. He is unsuccessful there, and after getting beaten for fighting with another boy he ends up fleeing to London where he catches the interest of the Artful Dodger, who takes him to Fagin the Fence. Fagin teaches him to be a pickpocket without his realizing it until he gets arrested, when a rich man named Brownlow takes pity on him and brings him home. Unfortunately, he gets kidnapped back by associates of Fagin. Oliver gets taken by one these associates, Bill Sikes to rob a house. Oliver gets hurt, the robbery botched, and the family takes him in. More complications result, including the mystery of Oliver's birth. In the end, he has a family.
As you can tell from this quick summary, the book is full of coincidences and odd events. Oliver is passed along like the ball in a sport, but he remains the innocent child throughout. He does not make choices. Things happen to him, rather than him making them happen. This was intentional on Dickens's part. He did not want Oliver to change, or be corrupted. He wanted him to remain innocent throughout.