The scientific method, as does much learning in general, begins with observation. Father Stanley Jaki likened this process to the first step in the march of science, without which there can be no second or third step. We might call it a sort of first cause in scientific investigation, both in order of time sequence an in order of importance.
Where do the models and theories come into all of this? The model is the second step (if observation and interpretation of data are together taken as one step), and that model should describe the system’s behavior and then predict its behavior under some new conditions. Then it’s a matter of testing the model—more observation and more interpretation—and then modifying it, and testing again, and so on. A theory then brings together several models in a coherent fashion and attempts to explain them.
Let’s take an example of observations and a model. Suppose I give you a set of squares which I have cut out and also a ruler. You set to work measuring the length of the squares, and then also measuring their perimeters. You find that the perimeter is always four times the length of the side. You build a simple model, which says P = 4L. Now I hand you a different set of rectangles, which are not squares. You measure the perimeter and short side, and find that the perimeter is not four times this length. The next step of the process is not to throw out the rectangles as if they never existed, or to decry this new data as “bad” . Rather, it is to modify the model, or (more appropriately) to add a new model which says that the perimeter will be P=2(L+H). I might next hand out a quadrilateral of some new configuration, and elicit a new model, and so on. The theory then is the synthesis of these models, and will be something like P = L1+L2+L3+L4, of which the rectangle and square are special cases. And if I encounter other figures (triangle, pentagons, hexagons, etc), the theory might be broadened still more to include these new figures, each of which has its own model within that theory.
But note that the whole process begins with observation, and only ends with understanding . Or so it should. Unfortunately, the mindset of many people, some Scientists (TM) included, is that the theory is all-important, and thus any observations which contradict that theory must be false observations. We witness this most prominently in in the argument over “climate change”  (Does it exist? What causes it: man, the sun, or some other factors? Is the world getting warmer or cooler? Is this a good thing?), in which all parties seem completely beholden to their own models (and funding sources).
They do this all the while failing to note that the models presented to do necessarily add up to a complete theory, let alone a good one. If Poincare was right when he likened science to a house and facts to bricks (as in, science is not just a bunch of facts any more than a house is just a pile of bricks), then we might note that if a good model makes use of and explain the observations in a particular scenario, then a good scientific theory makes use of the different models (or, for that matter, laws) by putting them in order (and, if necessary, reconciling them), just as the bricklayer not only cements certain bricks together to build a wall or make room for a window, but also arranges these features together to form a house.
I’m posting this on a Catholic site, so my readers may be wondering how all of this ties into our Faith. I began with Fr Jaki, and so I should return to him here, that is, return to an observation which he made. Many people dismiss the claims of the Church concerning miracles in general, especially the miracle of the Resurrection. They do this ostensibly because there is no room for miracles anywhere in their models of how the universe works . However, when models or even whole theories are found unable to account for facts, it is the theory which must be modified, not the facts observed. It is often the brick which is discarded which the house most needs as cornerstone.
 Bad, that is, “not good.” The data is fine as data. On the other hand, the new rectangles are not good as squares, because they are not squares. If they were meant to be, then they are not good examples of the category square in the Thomist’s accounting. On the other hand, they might be good as rectangles. Turn this on its head, and we say that the model used before for squares is not a good model for these new rectangles.
 Ends, that is, telos. The end of the scientific method is greater understanding, and if it does not arrive at this end, then to that extent it has been frustrated, whatever else we may accomplish. Of course, there was long ago a break from that end by such minds as Francis Bacon and Rene Descartes, who saw in science the possibility of controlling nature, which later lead to the even narrower understanding of science as “the process by which we develop new technologies and invent cool new gadgets.” The scientific revolutionaries sought to discard formal and final causes in favor of material causes; but these latter two suppose the former two, and are a bit less intelligible if divorced from them.
 Cue comment from Rick DeLano.
 They also view miracles as an actual breaking of the laws of nature, and (to paraphrase Fr Jaki again) they assert on “patently dogmatic grounds” that nature cannot change its course. But if God is the author of both miracles and nature, it seems to me conceivable that a miracle is not a disruption of nature, but a continuation of it which falls outside of our scientific theories.