Well the first thing you gotta know about Oskar Matzerath is that he's narrating this entire book from inside an insane asylum. He claims from the get-go that he can only remember the earliest parts of his life by drumming on his tin drum. As he takes us back, he decides that it's best if he starts with the story of how his grandparents first conceived his mother. Don't worry—it's a good story.
Next thing we know, Oskar's telling us that he was born with a completely functioning intellect. Shortly after his birth, a few comments by his parents make him decide that he never wants to grow up. So on his third birthday, he decides to stop growing. Literally. Oh yeah, and all he ever wants to do is obsessively play his tin drum. And pity the fool who tries to get between Oskar and his drum. The first time this happens, Oskar discovers another magical skill—he can shatter glass with his voice.
Oskar grows up (psychologically, not physically) during the rise of the Third Reich and Nazism. Times are certainly tough for anyone labeled as "different," so Oskar drums his way through life and shatters glass as a way of coping with his nutty family and the political events going on around him. He's convinced that he's a brilliant genius and he's got nothing but disdain for his family and friends who can't see beyond his childish appearance to his supernatural gifts. At a circus, he meets another little person who encourages him to learn to control other people before they control him. He takes this to heart and becomes a first-class manipulator. He plays the innocent child and gets away with some pretty horrible stuff.
At first, the war's distant and not really relevant to him, but it gradually gets closer until the Russians and Germans invade and pretty much destroy his city. After the war and the death of his parents, Oskar reluctantly decides to enter the adult world, gives up his drum, and begins to grow again. Unfortunately, he doesn't just grow taller, but he grows sideways and develops a huge hump on his chest.
Oskar moves to West Germany with what's left of his family, and has a series of bizarre adventures. He becomes the leader of a terrorist gang, gets a job engraving tombstones, works as a nude model at an art school, and eventually becomes a drummer in a jazz band. He goes on to a world-famous solo career where he uses his drum hypnotically to make people regress to their own childhood. Oskar has great luck with the women in spite of his small size and disfigured body. Despite all the bling and all the women, he gets exhausted by life in the adult world. He gets obsessed with a young nurse whom he's later convicted of murdering. It's pretty unlikely that Oskar's the murderer, but we do know that this is why he's narrating his life story from inside an insane asylum. (When he's apprehended, he claims to be Jesus. It's a great way to avoid prison, but don't try this at home.) He's relieved to be back in a place where he can act helpless and irresponsible.
By the end of the book, Oskar's thirty years old and spends his time hating his visitors, reminiscing about his past and telling us how special he is. He reflects on how Death has hovered over all the events in his life. He's probably going to be freed from the asylum, and wonders how he'll live the rest of his life with Death running behind him.