Mondas, Earth's twin, had an elliptical orbit that took it beyond the solar system. Far from the sun, the Mondasians began to weaken, but their scientists developed cybernetic techniques to compensate for this. Large numbers of Cybermen left Mondas, searching for a new home. They first encountered the Doctor when invading 'Planet 14' (mentioned in The Invasion), and then turned their attention to Earth in 1969 (The Doctor, perhaps accidentally, let slip about Nemesis' return to Earth, but later used this to his own advantage.)
Meanwhile, the (more primitive) Cybermen left behind on Mondas developed 'energy grabbing' technology, and began to install a gigantic propulsion unit on their planet (mentioned in Attack of the Cybermen). This brought Mondas back towards the Earth in 1986 (although the sun would surely have made a better power source). The Doctor encountered the Cybermen (from his point of view) for the first time, and the Mondasians were destroyed.
Having found out about the destruction of Mondas, in 1988 the Cybermen hatched a plan to use validium to turn Earth into the new Cyber planet (Silver Nemesis). Despite their thorough briefing (which included knowledge of Lady Peinforte) they were defeated by the seventh doctor, and the Cybermen experienced another huge setback to their plans for galactic conquest.
The Cybermen needed to establish a new base, and they decided upon Telos, the planet of the Cryons (Attack of the Cybermen). The Cryons were largely destroyed, and their cryogenic technology used to store an increasing number of Cybermen. However, the Cybermen were continually active elswehere.
In 2070 the second Doctor encountered another group of Cybermen (The Moonbase): according to The Tomb of the Cybermen, they were - in part - attempting to replenish supplies after the destruction of Mondas. In the 21st or early 22nd centuries the Cybermen hatched another plan, this time involving Station W3 (The Wheel in Space). Later the Cyber tombs on their adopted home of Telos were disturbed by the Doctor (The Tomb of the Cybermen).
In the 26th century a number of galactic powers united against the Cybermen. The Cybermen, starved of 'donors' and attacked with gold, were almost completely defeated The crew of a single Cyberman scoutship, ignorant of Telos, attempted to destroy Voga in the late 27th century (Revenge of the Cybermen), but was foiled by the fourth Doctor.
Forced to consolidate their position on Telos, the Cybermen, like the Daleks before them, began to experiment with time travel technology. However, their science was incapable of producing a functioning time machine. Instead, they stole a time machine from another, unknown race (Attack of the Cybermen), and plundered its secrets. Their first intervention was to travel to 1986 in order to save Mondas and destroy the Earth, ensuring that humans would never contribute to an alliance against it. When this failed 15,000 Cybermen travelled back to the 26th century in an abortive attempt to change the outcome of the Cyberwars (Earthshock). Perhaps this was the last ditch plan of a once powerful race.