Peter III was born Karl Peter of
Holstein in
1728. His mother was the daughter of
Peter the Great of
Russia and his second wife
Catherine I; his father was the nephew of the Queen of
Sweden and thus the baby had a claim to the
thrones of both countries. Peter's mother Anna died shortly after he was born, and his father when he was 11; for the next few years he was raised by his cousin Adolph. During his childhood, Peter's
father, who felt that he had a better claim to rule Sweden than the Queen and her husband, planted ideas of taking Sweden back again, and getting revenge on those who had taken the
crown. This seemed more likely than Peter getting any position in Russia, as his cousin the Empress
Anna disliked him. Peter had a Swedish
tutor who he hated and who humiliated him. Through his father and his tutor, Peter got the impression that
military strength was all-powerful, and the best models of military strength near him were the armies of
Prussia, who Peter tried to ape throughout his life.
In 1741, Empress Elizabeth seized the throne of Russia from her baby cousin Ivan VI. Elizabeth did not want to marry, so she chose Peter, whose mother had been her sister, to be her heir. In 1742, Peter came to Russia. (Shortly thereafter he was chosen as the Swedish heir, but it was too late -- he had been rebaptized in the Orthodox Church of Russia.) Elizabeth selected better tutors for her nephew, found him a wife (the niece of her dead fiance) who was baptized as Catherine, and tried to remold him into a satisfactory heir. Catherine and Peter got along at first, but after Peter's face was scarred from his attack of smallpox, Catherine is supposed to have flinched from him and Peter's hurt started a large rift between them.
Peter still preferred German culture to Russian, and wasn't that popular in his adopted country. Elizabeth urged them to produce a son to assure the succession, but it was several years until Paul was born, and rumors abound that he was the son of Catherine's lover rather than Peter. Elizabeth took Paul to raise, and Peter spent as much time as he could in his country retreat at Oranienbaum instead of with any family member.
Catherine later claimed that he preferred to play with toy soldiers, even when in a bedroom with his wife. This isn't too well confirmed by independent sources, but it is true that Peter was interested in all matters military, ordering European books on war and outfitting the soldiers under his command in Prussian-style uniforms (to their dismay). He wasn't good at staying still, and wanted to go back to Holstein and rule but Elizabeth would never let him. Instead, he made sarcastic remarks about people and Russian culture, which made him still more disliked by patriotic Russians.
When Elizabeth died in December 1761, Peter took the throne. In many ways he tried to keep on with the policies of his grandfather Peter the Great, who was also willing to model his armies on foreign examples. He tried to implement many reforms. But he made peace with Prussia, who Russia had fought to support Austria, a Russian ally. In itself this wasn't an unpopular idea; the war had been expensive. But the treaty made with Frederick of Prussia semed quite favorable to Prussia, even though Russia had been on top in the fighting. And Peter proposed to send the Russian army to Holstein to fight Denmark for some territory it had taken from Holstein. Most Russians couldn't care less about Holstein, so this idea was not well-received.
Peter had also become publicly estranged from Catherine, and flaunted his mistress, Elizabeth Vorontsov, in front of her. Catherine had accepted Russian culture rather than clinging to the German way of life, and was more popular than her husband. Peter had been warned that conspiracies existed to replace him with Catherine, but he didn't do anything that would stop her. If he had, he probably could have -- most of the army except for a few regiments, and at least some of the nobles, did support the legitimate Emperor. When Peter received word that with her small number of soldiers, Catherine had proclaimed herself ruler, he spent several hours trying to decide how to handle the situation, and in those several hours things went beyond stopping. Catherine had him arrested and got him to sign an abdication on 29 June 1762. (The abdication did not say who he was giving power to, and many probably thought that Catherine's rebellion was on behalf of their son Paul.)
Peter wanted to be allowed to go back to Holstein, and at first Catherine let him think he could. But he was kept in prison; among his guards were several of the Orlov brothers (Gregory Orlov was Catherine's lover at the time). Both Peter and the Orlovs were known to be hot-tempered, and they got in a fight. Alexei Orlov is apparently the man who actually killed Peter (at least, he wrote a letter to Catherine admitting responsibility and begging forgiveness), but the official story was that Peter had died of illness. Catherine the Great was now unopposed ruler, though several men pretending to be an escaped Peter III would lead rebellions in the south during her reign.
Sources: Donald Raleigh and A.A. Iskenderov's The Emperors and Empresses of Russia: Rediscovering the Romanovs and those listed in Monarchs of Russia.