I think this is the first thread I've started here, so it's a shame it's derivative of two topics of which this is only an important sub-topic. If this opening post is too long for you, focus on the red conclusions
, then work your way back to the premises
you disagree with, don't understand, or have a comment on--if you agree with the premises, but disagree with a conclusion, then explain how you think the argument is invalid. I will frequently post supporting links [#]
without referring to their content; I don't suggest reading them all unless the claim they're nearby interests you, because there are going to be a lot.
Please focus on criticizing these reasons, not arguing alternatives like Intelligent Design or talking about tangents like abiogenesis and metaphysics. I ask just because this topic is important enough to stand alone.
The same phenomenon under the same observed conditions is usually caused by the same process in the world.
* This is the basic premise of empirical inductive reasoning, and is a key to the scientific method in general.
Theories explain a phenomenon by delineating the process which causes it; a scientific theory generates predictions that can be falsified by the observation of an experiment.
C1-0) Theories are more likely to be true when valid experiments do not falsify them; when they successfully predict observations.
* Note that a theory is still called a theory, even when confirmed by valid experiment hundreds or millions of times, because P1-0 does not hold as a logical truth. Note also that you trust your lungs to breathe primarily due to P1-0.
Fossils are remnants of organisms 
Fossils formed across the last 3.8 billion years 
as determined by our ability to date them within a substantial degree of accuracy 
* We can also date some types of fossils and rock absolutely with raioisotope dating 
C1-1) Organisms have been on earth for at least 3.8 billion years and we know roughly when many types of them lived.
Fossils show specific groups living at specific times; with no fossils of humans, e.g., forming 3.8 billion years ago, and fossils of e.g. dinosaurs which are no longer extant today 
C2-1) Evolution, the changing and growing complexity of the form of life on earth, as well as vast extinction of life, has occurred over the last 3.8 billion years.
* Note that at this point I have made no conclusions about how
evolution has happened.
Organisms reproduce themselves using their genetic coding, usually DNA 
Reproduction of DNA (and RNA) molecules in biological systems often leads to small mutations or changes in the DNA molecule 
Changes in DNA can lead to changes in protein structure 
* This premise is often referred to as part of the "central dogma" of biology; that DNA is ultimately translated into amino acid sequences.
* While "dogma" may sound like a strong term, we have actually synthesized DNA from simple compounds and given it to bacteria--who then use that DNA 
* It is further standard practice to give bacterial cells particular DNA sequences to have them produce the protein encoded by that DNA 
C1-2) When organisms reproduce, sometimes mutations occur and lead offspring to have slightly different traits than the parent.
* This is partly an explanation of microevolution--note that bacteria can evolve both without the creation of 'new' genetic information 
and due to mutations that occur during recombination and DNA copying 
If an organism does not reproduce itself, it will eventually die and its genetic information will not be expressed.
* I think this follows deductively.
C1-3) If a mutation does not help an organism reproduce, there will not be any pressure for that change in genetic information to promulgate.
* This is microevolution by natural selection. We see it all the time in antibiotic-resistant bacteria.
Reproduction itself is governed by the expression of DNA.
Two populations of organisms that do not reproduce using one another's genetic material are of different species.
C1-4) Species can diverge due to the accumulation of gradual mutations.
* This has been explored on a genetic level for past eukaryotic species divergence events 
* This has been observed in the present tense for bacteria 
C2-4) Species can diverge due to reproductive pressure (from C1-3).
* This has been specifically observed in the present tense in many types of organism 
* This is the theory of evolution by natural selection.
Inferring using this with respect to the fossil record, we can further say:
C3-4) Evolution in the past can be explained as a consequence of species divergence due to reproductive pressure.
Obviously there's a lot more to explain; specific events that are shown by the fossil record still need to be explained. For example, why is it that change seems to occur sporadically, instead of all the time? For this particular point, there is a lot of evidence that genes are relatively stable without reproductive pressure; basically, the species under no pressure will only "wobble" genetically, on average staying the same 
. In fact the general view is that one would only expect change when reproductive pressure is in play; that punctuated equilibrium is unsurprising. (There's also the interesting application of this theory to our own species.) However, I think this discussion would be best suited to focus on disagreements with the above argument; more detailed applications can be discussed if the basic argument is ever finished.
Edit 1: Added P2-0 and C1-0. 12-22-2009 9:49 AM GMT
Edit 2: Added to P2-1 with three links about radioisotope dating. 12-26-2009 1:31 AM GMT