In the re-imagined series, Cylon basestars (also referred to as "baseships" or "Cylon battlestars") are by far the most prominent example of Cylon presence. They easily dwarf a Colonial battlestar and appear to be technologically superior in every way, including being able to release wings of hundreds of Cylon Raiders at the same time (according to the number of launch "slots" on the Basestar, it can release 792 Raiders as seen here, here, and here).
Beyond this, not much is known. Basestar operations would suggest that they have large crew complements, although there is ample evidence to suggest their operations are largely automated. Indeed, the large complement of Raiders would suggest on-board manufacturing facilities (The BSG Bible).
Its weapons complement indicates missiles on a similar principle to the United States' VLS system, which is capable of launching coventional or nuclear missiles.
Soon after the planet Kobol was discovered by battlestar Galactica, a basestar Jumped into orbit, resulting in the destrucion of two Raptors. Subsequently, Commander Adama devised a plan to destroy the basestar by using a Raptor fitted with a Cylon Transponder to sneak a nuclear warhead inside it. Pilot Lt. Sharon "Boomer" Valerii, a then-unknown Cylon sleeper agent, flew a Raptor along with ECO Lt. Margaret "Racetrack" Edmonson to infiltrate the inside of the basestar. While inside, they saw that basestars have a vast, cavernous interior made of bio-mechanical components, without a distinct floor or ceiling. The walls appear fleshy and alive, similar to the synthetic organs filling the interior of a Raider. Also of not is that the Basestar was pressurized, as the Raptor appeared to enter through a ventricle-like airlock and Boomer was able to speak with her helmet removed, a task made impossible in a vacuum.
Boomer and Racetrack successfully detonated the nuclear warhead, completely destroying the basestar. This was perhaps the first time since the Cylon Attack that Colonial forces successfully destroyed a basestar.
Shortly thereafter, Valerii's sleeping Cylon programming apparently activated, compelling her to shoot Commander Adama in an assassination attempt (Kobol's Last Gleaming, Part II). She was subsequently killed by Specialist Cally. Consequently, Edmonson is now the only living member of Galactica's crew that has ever seen the inside of a basestar (Resistance).