Some exciting work has been done in the philosophy of causation over the past 20 or so years. Most of it coming from cognitive and computer scientists. They have developed some sophisticated tools for constructing causal models.
The apotheosis of this effort is probably manifested in the work of Judea Pearl. However, Pearl's work is not for the faint-hearted.
Steve Sloman's book Causal Models: How People think about the World and its Alternatives offers a more manageable introduction to some of the key ideas. It is also of interest to me because it covers some of the psychological research on how people reason about causality.
I've decided to go through Sloman's discussion of the basic elements of causal modeling. The discussion is found in Chapters 3, 4 and 5 of his book.
Chapter 4: Causal Models
Chapter 5: Observation v. Action