Cyber-conversion
Cyber-conversion was the physical and mental re-engineering of victims, often humanoid, into Cybermen. In an alternate universe, this was referred to as upgrading. A similar process used by the Borg from a parallel universe was called assimilation.
Cybermen of Mondas
Mondasian cyber-conversion involved the replacement of body parts (including limbs, organs, and vital systems) with artificial components. (TV: Attack of the Cybermen) Partial conversion, with the victim retaining autonomy and a human identity and body parts, was possible. (TV: The Invasion)
The Cybermen would traverse the universe to find beings to convert, adding to their forces. (TV: Attack of the Cybermen) The Cybermen relied on tubing to keep the body operating, but over time the amount needed decreased. (TV: The Tenth Planet onwards)
The Cybermen who recovered from the Cyber-Wars and formed the Cyberiad possessed the most advanced technology used by Cybermen, and this extended to their conversion technology. Cyber-conversions could be carried out at almost any time, even in the midst of battle. Cybermites, an advanced form of Cybermat, could attack organic beings and graft technology that converted the being's mind to that of a Cyberman, with full conversion of the body presumably being carried out later. Cyberiad technology had also overcome a major flaw of previous Cyber-conversion techniques; the reliance on exclusively Human or Mondasian stock. The Cyberiad were able to convert all organic life forms, even Time Lords, into Cybermen, meaning that the Cyberiad could create more Cybermen than had been possible for the other groups of Cybermen.
The method used for the full conversion of a victim's body is unclear, and may have been different depending on which species was being converted. The partially-converted body of Webley seems to show that Humans are converted by encasing the body within a cyber-suit. However, a fully-converted Cyberman was able to remove it's head entirely to trick a Human soldier. This Cyberman may have originally been a non-humanoid, however. (TV: Nightmare in Silver)
Cybermen of Pete's World
The Cybermen of Pete's World, instead of replacing body parts, transplanted living brains into metal exoskeletons sustained in a cradle of chemicals and threaded together by an artificial nervous system. The process was extremely painful and took place in a booth where the subject's skull was sliced open by a robotic machine that used knives, lasers and syringes to remove the brain before encasing it in an empty cybernetic helmet. Later, the Ear Pods created a trance state for the victim, so they were, in a sense, unconscious during the process and unable to feel the pain of being converted due to the EarPods having control over the brain's pain receptors. This was the most efficient form of conversion as it took under 60 seconds. They also had an emotional inhibitor placed within them to suppress their humanity because, as the Tenth Doctor put it:
It's still got a human brain; imagine its reaction if it could see itself. Realise itself inside this thing. They'd go insane.
During the Battle of Canary Wharf, the Cybermen, badly needing reinforcements, quickly converted humans into Cybermen using a different method. They encased humans in cybernetic shells by constructing the suit of armour around their body, as with Lisa Hallett. Hallett would have died if her lover, Ianto Jones, had not retrofitted a cyber-conversion unit into life support for her. This form of conversion was excruciating. The subjects were heard screaming as metal was grafted onto their flesh, possibly because the Cybermen had little time to place their victims in a trance state. (TV: Cyberwoman)
The Cybermen also employed a very primitive type of conversion in 1851 when they created the Cybershades using scrap metal and Victorian era human technology. They also invented a method of converting humans into command units for CyberKings by fitting them with a headset that could take control of their brains. The CyberKing was intended as a mass conversion unit, but the command unit Miss Hartigan, aided by the Tenth Doctor, destroyed it before it was put to use. (TV: The Next Doctor)
A Cyberman's exo-skeleton in 102 at Stonehenge displayed the ability to upgrade humans without any external machinery, merely needing to restrain the victim while the Cyberman's faceplate split open at the middle and enveloped the victim's head. The process from here on is unknown, as the only known victim of this process was Amy Pond, who escaped before the process was completed. (TV: The Pandorica Opens) The human that was previously converted seemed to have an upgrade like that during the Battle of Canary Wharf, due to the fact that the Canary Wharf upgrade involved encasing the body inside the suit, (TV: Cyberwoman) while this Cyberman had a severed head in its helmet. (TV: The Pandorica Opens)
As the Cybermen continue to upgrade themselves technologically, it is logical that the methods used to convert victims would itself be constantly modified, thus these differences in conversion should not be considered contradictory.
Named cyber-converted individuals
Cybermen of Mondas
The first known Cybermen, if not the first, Zheng was converted as part of the Mondasian effort to steer their planet away from the destructive cherrybowl nebula, and back to Sol, with a propulsion system on the surface. Like other early Cybermen, Zheng retained his name, as Cybermen were regarded as still being individuals by their creators. Unlike other early Cybermen, however, Zheng was not affected by organ rejection, a problem which affected the Cybermen until they learnt of a way of avoiding it by scanning and copying part of the physiology of the Fifth Doctor, specifically a lobe in his brain that dealt with all bodily functions. Before this, however, he was unique in surviving for so long, and he was made Cyber-commander. Zheng was more resilient than other Cybermen, being able to survive being shot by another Cyberman on the orders of the first Cyber-Planner, (AUDIO: Spare Parts) and still functioned well after all Mondasians were converted. (AUDIO: The Reaping)
The Mondasien Chang Twins joined the surface work crews, and were converted into Cybermen. (AUDIO: Spare Parts) Mondasien teenager Eric Krailford either volunteered to join or was drafted into the surface work teams, and was converted. (AUDIO: Spare Parts) As a Cyberman, he retained part of his name, and became Krail. In 1986, he led the first force of Cybermen to land on Earth in the occupation of Snowcap base, and was killed by General Cutler. (TV: The Tenth Planet)
After being drafted by the Mondasian government to work on the propulsion system, Yvonne Hartley was mostly converted. Conversion was stopped by loss of power caused by proximity to the cherrybowl nebula, and Yvonne wandered back to her home, due to her pre-conversion desire for her Father to see her 'uniform'. Enough of her individuality survived for her to recognise her Father and her pet Cybernetic bird. When power was restored, her conversion continued automatically. Away from the hospital used for conversions, the process killed her. (AUDIO: Spare Parts)
Sisterman Constant was originally responsible for draughting Mondasians for conversion, but was injured when a partially converted Cyberman tried to force her to divulge their purpose. Cyber-commander Zheng shot the Cyberman, and, noting that her scapula was fractured, sent both the Cyberman he had shot and Constant to be repaired. Despite her protests, Constant was converted, and as a Cyberman advocated full conversion of Mondas. (AUDIO: Spare Parts)
Thomas Dodd, the owner of a store selling replacement organs and limbs, was captured by the Cybermen while trying to help the Fifth Doctor. He was converted, becoming the first Cyberman to be augmented with an additional lobe, based on that found in the Doctor's brain, that dealt with bodily functions and prevented organ rejection. (AUDIO: Spare Parts) Toberman was Partially converted on Telos with his right arm replaced. He regained his humanity and attacked the Cyber-Controller. He gave his life to close doors of the Cybermen's tombs (TV: The Tomb of the Cybermen)
Bates and Stratton, when Cyber-converted, found it failed at an early stage after their limbs had been replaced by mechanical equivalents. They put to work on the surface of Telos with similar such failures. Lytton was Partially converted cyber on Telos, still incomplete at the time of his death. Others notably converted were Bill and David. (TV: Attack of the Cybermen)
In a divergent timeline, Evelyn Smythe, Nicola Savage, Ricky Allen, Ryan Carey and David Isherwood were all partially converted. Reece Goddard became a skin drone. (WC: Real Time, AUDIO: Real Time)
Tobias Vaughn suffered partial cyber-conversion, retaining just his head and therefore his own thoughts. (TV: The Invasion)
Jason Kane was nearly converted after being manipulated by Irving Braxiatel. Before the conversion was complete, however, Bernice Summerfield used the energy in the Crystal of Cantus to defeat the cybermen, reversing the conversion. (AUDIO: The Crystal of Cantus)
Webley was partially converted by cyber mites. He retained most of his body and, based on speech, some emotions as well. Artie Maitland and Angie Maitland suffered partial conversion by Cybermites, who intended to take advantage of their imagination. The conversion was later reversed. A pair of soldiers were partially converted while in combat with a Cyberman. The Eleventh Doctor was Partially converted into a Cyber-Planner, splitting his mind into two halves; one was normal, the other converted. The Cyber-planner half showed emotion. The Doctor suggested that to decide who controlled the brain, they play chess, to which the Cyber-planner agreed. After distracting the Cyber-planner by lying about being able to win the game with only three moves, the Doctor used his sonic screwdriver to remove the cybernetic implants, freeing his mind. (TV: Nightmare in Silver)
Bill Potts, after being mortally wounded, was taken to a hospital on a Mondasian colony ship and was granted a cybernetic heart then fully converted into a Mondasian Cyberman some years later. Prior to her full conversion, she was unable to survive if she did not remain in the hospital. (TV: World Enough and Time)
Cybermen of Pete's World
John Lumic was converted into a Cyber-Controller, while numerous others such as Sally Phelan and Jackie Tyler were converted into regular Cybermen. (TV: The Age of Steel)
Yvonne Hartman, a Torchwood Institute administrator, was converted. She retained her free will though, killing several Cybermen before her death. (TV: Doomsday) Another Torchwood employee, Lisa Hallett, the lover of Ianto Jones, was partially cyber-converted (TV: Cyberwoman)
Mercy Hartigan was the CyberKing command unit. Miss Hartigan refused to be converted to a standard Cyberman and took control of the Cybermen which landed in 1851. The Cybermen, however, had slowly set a plan in motion that would eventually make Miss Hartigan both a convert and a leader. (TV: The Next Doctor) There was also Valerie Brannigan. (COMIC: In-Flight Entertainment)
Cybermen of the Cyber Legions
Several people (namely Shona, George, Atif Ghosh and Sheila Clark) were converted by the Cybermen of a crashed ship as they attempted to find a suitable Cybercontroller. They eventually chose Craig Owens but the conversion failed when Craig's paternal instincts were triggered by his son's crying. (TV: Closing Time)
Cybermen created by Missy
Missy transformed the dead corpses of millions of humans into Cybermen, such as Alistair Gordon Lethbridge-Stewart, Danny Pink and Skarosa. They were eventually destroyed when Danny detonated all of them to stop Missy's plans, save for Stewart, who shot Missy personally before being saluted by the Twelfth Doctor. (TV: Death in Heaven)