Voldemort does not appear in Harry Potter and the Half-Blood Prince, although his presence and actions are felt: he once again declares war, and begins to rise to power once more. He murders Amelia Bones of the Department of Magical Law Enforcement, and begins to target members of the Order of the Phoenix, including Emmeline Vance.  Rowling uses several chapters as exposition to establish Voldemort's backstory. In a series of flashbacks, using the pensieve as a plot device, she reveals that Voldemort was the son of the witch Merope Gaunt and a Muggle called Tom Riddle. Riddle abandoned Merope before their child's birth, soon after which Merope died, just hours after giving birth. After living in an orphanage, young Riddle met Dumbledore, who told him he was a wizard and arranged for him to attend Hogwarts. Riddle was outwardly a model student, but was in reality a psychopath who takes sadistic pleasure in using his powers to harm and control people. He eventually murdered his father and grandparents as revenge for abandoning him. The book also discusses Riddle's hatred of "Muggles", his obsession with Horcruxes, and his desire to split his soul to achieve immortality. Rowling stated Voldemort's conception under the influence of a love potion symbolises the prejudicial circumstances under which he was brought into the world.  In the main plot of the book, Voldemort's next step is to engineer an assault on Hogwarts, and to attack Dumbledore. This is accomplished by Draco Malfoy, who arranges transportation of Death Eaters into Hogwarts by a pair of Vanishing Cabinets, which bypass the extensive protective enchantments placed around the school. The cabinets allow Voldemort's Death Eaters to enter Hogwarts, where battle commences and Dumbledore is cornered. Hogwarts professor (and re-doubled agent) Severus Snape uses the Killing Curse against Dumbledore when Draco could not force himself to do so.

Answer this question "What happens as he gains power?" by extracting the answer from the text above.
He murders Amelia Bones of the Department of Magical Law Enforcement, and begins to target members of the Order of the Phoenix, including Emmeline Vance.