Count Dooku was a respected Jedi in his youth, and a student of Yoda's. As a Jedi Knight, he gained a reputation for unabashedly expressing his own views on knighthood and the Force, which often differed with his fellow Jedis' views. However, he was still highly respected.
He passed on many of his views to his apprentice, Qui-Gon Jinn, who would later grow up to be mentor to Obi-Wan Kenobi. Sadly, Qui-Gon was the first casualty in the resurgence of the Sith: he was killed by Darth Maul, who was subsequently killed by Obi-Wan. Dooku was angered by the Jedi Order's failure to protect its own, and angrily resigned from the order.
Soon afterwards, he was confronted by Nute Gunray, the viceroy of the Trade Federation, who told him that in blockading Naboo, they had been following the instructions of the Sith Lord, Darth Sidious. Investigating further, Dooku learned that Sidious was in fact the newly-elected Chancellor Palpatine. Confronting Sidious directly, Dooku found that Palpatine appeared to share many of his views about fixing the Republic and reforming the Jedi Order. Palpatine convinced Dooku to become his apprentice, and gave him the name Darth Tyranus.
To show one's absolute loyalty to the Sith, a new apprentice must kill someone close to him. Dooku chose to kill Sifo-Dyas, a Jedi Master who had recently shared with Dooku an order he had placed on Kamino for a clone army. Dooku and Palpatine decided this army would be useful for the Republic. Dooku took Sifo-Dyas's place as liaison with the Kaminoans, and hired bounty hunter Jango Fett to be the genetic template for the army.
Having the military force they needed under development, Palpatine and Dooku also needed the political climate to justify its use. Dooku would prove instrumental in instigating a separatist movement that would argue for seceding from the Republic to escape Palpatine's ineffective administration.
Eight years after his turn to the Dark Side, Dooku returned to public life. To respond to the separatist crisis, Palpatine was allowed to stay in office. Dooku was also mobilizing a droid army to attack the Republic. When Obi-Wan Kenobi discovered the army, he was captured and sentenced to die on the Geonosis arena. As predicted, the Senate gave Palpatine emergency powers to respond to the crisis, and take possession of the clone army. The battle to save Obi-Wan became the first battle of the Clone War. As he attempted to escape Geonosis, Dooku was confronted by Obi-Wan Kenobi; whom he wounded; and Anakin Skywalker; whose right arm he cut off at the elbow. He then fought Yoda, but threw a piece of machinery at the other injured Jedi to distract Yoda and escape in the meantime.
Three years later, Palpatine had amassed enough political power that he was ready to end the war and declare his Empire. But he also wanted the gifted young Jedi, Anakin Skywalker, to join the ranks of the Sith. Dooku was led to believe that Anakin would lead an army of Sith that would be formed from the remnants of the Jedi Order, and so was willing to go along with Palpatine's plan to lure him to the Dark Side: Palpatine himself would be kidnapped by the Separatists, and Anakin Skywalker and Obi-Wan Kenobi would be the only Jedi close enough to rescue him before the Separatists left Coruscant airspace. Dooku would then kill Obi-Wan, which would anger Anakin enough to make him turn to the Dark Side. Skywalker and Kenobi arrived as expected, but Dooku's attempt to kill Obi-Wan only knocked him unconscious. It had the desired affect on Anakin, however, who attacked Dooku with a new fury, culminating in him cutting off both of Dooku's arms. Not until this point, when it was too late, did Dooku realize that Palpatine had no interest in keeping him on as an apprentice. He was merely to be served up as bait to Anakin Skywalker. Dooku was shocked and speechless when Palpatine, whom he had expected to come to his defence, instead told Anakin to kill him. Despite his initial reluctance, Anakin gives in to Palpatine's goadings and decapitates Dooku.