As a second miracle was approved earlier this year, it's likely that Bl. John Henry Newman will be canonized later this year, so it seems appropriate to say something about Newman on development of doctrine because (1) people are likely to be talking about development of doctrine using Newman as their authority and (2) Newman's account of development in An Essay on the Development of Christian Doctrine is very often misunderstood. If the past is any indication, it's particularly likely that people will try to appeal to Newman for significant changes in doctrine, incorrectly calling it 'development', so it's probably worthwhile to start insisting that it is incorrect now rather than later.
There are two things that need to be grasped to understand An Essay on the Development of Christian Doctrine; failure to recognize them leads inevitably to misinterpretation.
First, the essay does not give a Catholic theory of doctrinal development but an Anglo-Catholic one. Newman was an Anglican when he wrote it. This is not to say that there's anything in it that is, properly understood, inconsistent with Catholic doctrine, but Catholic doctrine, in the sense of that doctrine connected to communion with Rome, is its conclusion, not its foundation. The argument itself is developed in Anglican terms, with Butler as the primary authoritative guide, and the account of doctrine given in it is also in Anglican terms, although primarily from the Catholic-friendly side of the Anglican heritage. And the problem the essay addresses is an Anglo-Catholic problem that only arises in an Anglican context, namely, that the Catholic Church has much to recommend it as a preserver of doctrine but seems to go beyond what one can find explicitly in the Apostles and the Fathers, and is, so to speak, under accusation of having distorted the true faith. What Newman primarily concludes in the essay is that there is no argument on Anglican principles that would make Rome guilty of this accusation that would not also establish that the Church of England is guilty of the same thing. As Newman was already convinced, on Anglo-Catholic principles, that Protestantism was wrong, and the argument and convinced him that the Church of England was unable to function as the Via Media, the middle way between Protestantism and Rome, that he had thought, it dissolved the last major intellectual issues that prevented Newman from becoming Catholic.
Second, and relatedly, despite the prominence of the notion of development, it is not the primary concern of the argument. Apparent change of doctrine can be either a development or a corruption, and, structurally speaking, the primary concern of the essay is not development but distinguishing developments from corruption. If you ever come across anybody appealing to Newman about development of doctrine and not showing a significant concern for the importance of avoiding corruption, that is a serious red flag; it is a warning sign that you are probably getting a distortion of Newman.
The essay falls into major parts. The first gives a broadly Butlerian argument (i.e., based on the analogy of nature) that developments of doctrine are natural and to be expected, and confirmed to occur historically; the primary purpose of it is to explain what he means by development and to give a basic characterization of Catholic developments of doctrine, 'Catholic' being here understood in the Anglo-Catholic sense of what we find in the commonly accepted Church Fathers. As he puts it, "Christian doctrine admits of formal, legitimate, and true developments, that is, of developments contemplated by its Divine Author." This is quite important: the only things that Newman considers "formal, legitimate, and true developments" are those that are already in some way implicit in the original teaching; to recognize something as a genuine development of Christian doctrine, rather than a corruption, is to identify what there is in it that gives you reason to think that it is a living expression of the teaching received from the Apostles.
This sets up the second major part of the essay, which attempts to characterize what a living expression of apostolic teaching would be. Newman uses the analogy of a living versus a decaying body; the living body has certain characteristics to show that its growth is a growth of the body itself, whereas the decaying body is a dissolution of the body itself. On this basis he identifies seven Notes of Development, that is marks that we are dealing with the living development of the Church and not its disintegration. These seven Notes are not all equally important, but they are all intended to be quite general -- that is, it's not a theory that is concerned solely with Church doctrine but with the healthy development or the decay and corruption of any idea at all. (It is important to Newman that his account have nothing of the ad hoc to it, so it's also important for the basic ideas to apply quite generally.) Because these Notes are attempts to differentiate the living of an idea from its dying, it's actually best to think of them as seven ways in which we can say that a doctrine, despite apparent change, is nonetheless the same. (It is also a major warning sign if people talk about 'development of doctrine' and make no effort to establish the way in which the supposed development is the same doctrine rather than their own replacement of it.) Newman himself often puts it in these terms: "There is no corruption if it retains one and the same type, the same principles, the same organization; if its beginnings anticipate its subsequent phases, and its later phenomena protect and subserve its earlier; if it has a power of assimilation and revival, and a vigorous action from first to last." Another name he gives to these marks is "Notes of fidelity in intellectual developments".
(1) Preservation of Type: If Y develops from X, Y must be the same type as X. All ideas have implications or expressions that are not at first explicit, but which can be recognized as having the same character as the original. Newman argues on historical grounds that the type that we see exhibited in the original teaching of the Apostles, and later in the Church Fathers, has very general but nonetheless identifiable characteristics (recognizable at first sight), all of which are most particularly shared by the Christian churches in communion with Rome. Thus the doctrines of the latter are occurring within a context that is consistent with the original characteristics, at least at a general level, of the Apostolic and Patristic teaching.
(2) Continuity of Principles: If Y develops from X, Y must derive its root content from X. Examples Newman mentions of principles that are relevant to the Christian faith are: dogma ("supernatural truths irrevocably committed to human language, imperfect because it is human, but definitive and necessary because given from above"), faith (acceptance of such truths with internal assent not involving sight or knowledge), theology, sacrament, Scripture including its mystical or allegorical sense, grace, asceticism, the malignity of sin, the possibility of sanctification.
(3) Assimilative Power: If Y develops from X, then in its growth from X, it must incorporate from its environment what is consistent with and appropriate to X, transmuting or rejecting the rest. That is, a living idea will necessarily absorb things from its environment, but anything that is absorbed is assimilated to it; it is not modified in order to fit arbitrary things it meets in its environment. The things it gets from its environment are unified in it, rather than its being disrupted by the environment.
(4) Logical Sequence: If Y develops from X, there must be some path, capable of being reasoned, from X to Y. This need not be strict logical deduction, although that, of course, is one kind of relevant pathway; that Y is appropriate given X is another kind of relevant pathway. Newman gives as an example Peter's extension of baptism to the Gentiles on the grounds that as Cornelius and his friends had already received the Holy Spirit (i.e., for baptism) it would be absurd to deny them water for baptism.
(5) Anticipation of Future: If Y develops from X, then there must be things that can be found in X that already pointed to or suggested what we find in Y. Thus, for instance, the Christian view of the body and of the resurrection and the honor given to martyrs that we find in our earliest depictions of Christianity already suggest some of the things that we find in Catholic veneration of relics. While Newman doesn't use it as an example, I think the Second Council of Nicaea on icons is a good example: an important aspect of the argument of the Council is that the Incarnation, in and of itself, gives a reason to reject iconclasm -- if Christ was truly Man, then he can truly be depicted as Man, and our regard for His picture, like our regard for the picture of a man, carries our attention to the Man depicted. Thus the essential principles laid down in the doctrine of the Incarnation are as it were recapitulated in a new context by the doctrine of icons; you can find in the doctrine of the Incarnation the things that suggest what one finds in the doctrine of icons.
(6) Conservative Action: If Y develops from X, then Y should come about in an attempt to preserve X. Thus for instance, all of the doctrine of the Incarnation we find in the early Ecumenical Councils are attempts to preserve what had been received.
(7) Chronic Vigor: If y develops from X as a living expression, then Y should have the same active life as X, either continuously or recurrently over long periods of time. Vigorous corruptions flare up and then die out; lasting corruptions grow weak and decay. Only the living thing is renewed in its active influence again and again. Thus, Newman argues, the resilience of the Catholic Church is a sign that its doctrine and worship are not in any essential way corrupt -- it is the behavior of something that is living rather than rotting.
The ways in which these seven interact is diverse and complicated, and Newman gives many, many examples in the essay. But, as he notes, "It would be the work of a life to apply the Theory of Developments so carefully to the writings of the Fathers, and to the history of controversies and councils, as thereby to vindicate the reasonableness of every decision of Rome"; the whole essay is just a gesture at this, a first argument that such a vindication could very well be possible.