How was Pelagianism originally formally defined?

The heresy of Pelagius was summarized by John Cassian in the 5th century:

At any rate we think that this fact ought not to be omitted, which was special and peculiar to that heresy mentioned above which sprang from the error of Pelagius; viz., that in saying that Jesus Christ had lived as a mere man without any stain of sin, they actually went so far as to declare that men could also be without sin if they liked. For they imagined that it followed that if Jesus Christ being a mere man was without sin, all men also could without the help of God be whatever He as a mere man without participating in the Godhead, could be. And so they made out that there was no difference between any man and our Lord Jesus Christ, as any man could by effort and striving obtain just the same as Christ had obtained by His earnestness and efforts. Whence it resulted that they broke out into a more grievous and unnatural madness, and said that our Lord Jesus Christ had come into this world not to bring redemption to mankind but to give an example of good works, to wit, that men, by following His teaching, and by walking along the same path of virtue, might arrive at the same reward of virtue: thus destroying, as far as they could, all the good of His sacred advent and all the grace of Divine redemption, as they declared that men could by their own lives obtain just that which God had wrought by dying for man’s salvation. They added as well that our Lord and Saviour became the Christ after His Baptism, and God after His Resurrection, tracing the former to the mystery of His anointing, the latter to the merits of His Passion.

Against Nestorius, Book I, Chapter III

Cassian connected the Nestorian heresy closely with the Pelagian:

Whence this new author of a heresy that is not new, who declares that our Lord and Saviour was born a mere man, observes that he says exactly the same thing which the Pelagians said before him, and allows that it follows from his error that as he asserts that our Lord Jesus Christ lived as a mere man entirely without sin, so he must maintain in his blasphemy that all men can of themselves be without sin, nor would he admit that our Lord’s redemption was a thing needful for His example, since men can (as they say) reach the heavenly kingdom by their own exertions. Nor is there any doubt about this, as the thing itself shows us. For hence it comes that he encourages the complaints of the Pelagians by his intervention, and introduces their case into his writings, because he cleverly or (to speak more truly) cunningly patronizes them and by his wicked liking for them recommends their mischievous teaching which is akin to his own, for he is well aware that he is of the same opinion and of the same spirit, and therefore is distressed that a heresy akin to his own has been cast out of the church, as he knows that it is entirely allied to his own in wickedness.

Ibid.

As has been noted in another answer, certain points of Pelagius were specifically condemned by the canons of a local synod of bishops in Carthage in 418. These canons were later accepted by the eastern Sees in a single body through Canon II of the "Quinisext" Council of Trullo in 692.

As an aside, Bede, in his Ecclesiastical History of Britain, noted that a form of Pelagianism persisted into the 8th century in Ireland. One might argue that Pelagianism thrives today in the belief, as John Cassian put it 15 centuries ago, that Jesus "had come into this world not to bring redemption to mankind but to give an example of good works."