It is acquired as an extrinsic through putting on a ring of regeneration or wielding the Healer's quest artifact, the Staff of Aesculapius. It can only be acquired as an intrinsic by eating a ring of regeneration if the ring is of suitable material and you are polymorphed into a monster that can eat it, or by polymorphing into a monster with innate regeneration: all vampires, vampire bats, werecreatures, imps, lemures, quasits, all trolls, all liches, Archons, the Wizard of Yendor and Riders.
Regeneration also burns nutrition faster; namely, one point of it every odd turn, unless the source is an artifact. Note that a digested ring of regeneration will use nutrition. This may be a good or a bad thing, depending on whether there is a scarcity of food or a corpse that you wish to eat; the former tends to be the case in the early game, whereas the latter situation is common in the late game.