A rough and approximate summary of William Whewell's view of the scientific method:
1. Common observation
2. Collection of instances
a) by observation if regular
b) by experiment if occasional
3. Decomposition of phenomena
a) via analogy
b) via simple connections
4. Classification and development of terms
5. First induction
a) of class-describing propositions in observation
b) of laws of phenomena in experiment
6. Second induction (causes of laws)
The idea is (again, roughly) this. We go about in our everyday lives observing the world, drawing conclusions about it (1); then someone says of something, "Hey, that's interesting," so begins to look more closely and systematically at what happens (2). To understand what is going on, we can't have mere data; we need a phenomenon, i.e., something fairly stable with regard to which we can draw general conclusions. Some natural data (for instance, those of traditional astronomy) are so stable that they are phenomena already, and so the trick there is just to find a way to observe them (2a). Others, however, are harder to pin down, and need to be studied under a set of controls (2b). Once we have recognized a phenomenon, we need to do some analysis of it (3) and in so doing we begin to develop a cogent way of talking and thinking about the phenomenon, adequate to our purposes (4). Then we begin what Whewell calls 'induction', but which we really should call 'superinduction', because as he understands it, it involves the superinducing of concepts on the phenomena; this involves identifying what a set of facts share in order to construct general principles or laws (i.e., stable general propositions) of the phenomena (5). After this we can take the process up another notch in order to explain the laws in terms of the causes on which they are based (6).
As I noted above, all this is a rough approximation. But it conveys, I think, a bit of why, despite having been dead almost a hundred forty years (Whewell's dates are 1794-1866), Whewell is my favorite philosopher of science: he is well-informed, balanced, and thorough, and recognizes that 'doing science' doesn't consist of one thing but of many different sorts of things that tend in a general direction (i.e., toward theories that are predictive and coherent and that allow us to understand unities in the world that might otherwise be missed). Indeed, while there has been good work in philosophy of science this past century, I find it difficult to find anything that really holds a candle to Whewell. Duhem comes closest, I suppose; but even he seems a bit simplistic when set beside Whewell. If you go into philosophy of science, Whewell's still the man to improve upon. For further information about Whewell, see this article.