Shinzon is a spectacularly stupid clone of Jean-Luc Picard made by the Romulans for the purpose of infiltrating the Federation. The plan was scrapped, and Shinzon was sent into slave labor in the dilithium mines on Remus. His only appearance is in Star Trek: Nemesis as the shitty movie's shitty main villain.
Shinzon managed to collect several weapons and a following of Remans to take over the Romulan senate. These weapons included an exceptionally advanced starship called the Scimitar and a "thalaron radiation" weapon that could kill large numbers of people even in small doses. He planned to use these to exterminate humanity for reasons that were never fully explained. He began by killing off the senate with a small thalaron bomb that they, in an act of great stupidity, allowed him to bring into the senate chamber.
Shinzon was designed to have his aging accelerated so he could replace Picard. After the plot was scrapped, his age was never accelerated. Because of this, he developed a life-threatening illness that only a complete transfusion of blood from Picard could cure. Although he will die within a couple of days, he keeps Picard and the Enterprise-E waiting in orbit around Romulus for 17 hours, then invites Picard and company to dinner the next day, at which point he wastes more time telling everyone his sad life story and then mind-rapes Deanna Troi for no logical reason, all before kidnapping Picard (one wonders if this is where DarkStar got his inspiration for his Sullust-to-Endor time figures), only to have Picard rescued with a transporter.
Shinzon's combat tactics show as much intelligence as his prioritization of capturing Picard. He has a "perfect" cloak on his ship, yet approaches so close to his opponents that they can still hit it firing blind. Once the Enterprise-E is crippled, Shinzon decloaks and sits right in front of them. A group of Reman troops beams aboard the Enterprise-E, emerging not in any critical portions of the ship but in a random corridor. Picard orders a ramming course and Shinzon's response is to order "hard to port", thus making sure the Scimitar does not use its main engines to try to avoid the collision. The attempt fails and the Enterprise collides with the Scimitar, heavily damaging both ships.
Picard engages Shinzon in hand-to-hand combat onboard the Scimitar in what is supposed to be the big climactic fight. In the crowning stupidity, Picard holds a long pole (much too large to be moved with any significant speed in a fight) straight out in front of him, and Shinzon simply runs straight onto it.
In short, Shinzon is one of the biggest morons ever seen in Star Trek.