The question to be asked is what interpretation best explains the evidence that we observe. As new information comes in, it will either support your interpretation or contradict it. Support tells you that you are on the right track. Contradiction tells you that you need to rethink your theory.
The first observation that gets discussed is morphology. Now if we look at the animals that are alive today and the animals that the fossil record tells us were alive in the past, we see that the form a nested heirarchy. All by itself this could mean that all of these animals were produced by common descent or by common designer. (As a note, I am not trying to set up a false dilemma here. I recognize that there may be other explanations that could be put forward but I am purposely restricting the discussion to the two possibilities under discussion.) So you have to go to the next observation.
The next most obvious observation is genetic. If you examine all the different types of genetic material that has been tested and use it to construct phylogenic trees, you find that you get much the same pattern as you do when you arrange the fossils by morphology. Let's see how these observations stack up.
One easy test is to look at just the functional genes. These can again be used to support common descent or a common designer. Both will claim that creatures that are the most similar should have the most similar DNA.
But you can start to untangle the two by looking into further types of genetic material that is not related to the functional part of DNA. One example would be to look at retroviral inserts. These happen when a virus inserts part of its genome into its host. If this happens in a reproductive cell, then the genome of the virus can be passed on to the offspring. Since this has nothing to do with the functional part of the genome, it can shed light on the situation for us. For example, if common descent were true, then you would expect the retroviral DNA to show the same pattern as the other lines of observation. If a common designer were the true explanation, then you would expect a random distribution of the retroviral inserts when compared between the species. In fact, you see that the pattern follws that which wbe expected of common descent. The common designer option cannot explain this pattern.
If you take the retroviral discussion and repeat it with things like paralogs, pseudogenes, retrotransposons and such you will find the same result. One pattern would be predicted by common descent and another by a common designer but the patterns only fit that of common descent. For example, whales have a complete set of psuedogenes identical to what land based animals possess for their sence of smell. If whales evolved from land based ancestors, this is easily explained. But if they were recently created as is, there is no reason for them to possess such useless genes. A common designer advocate is forced into giving an arbitrary, ad-hoc explanation for this observation.
From here let's move on to other topics. Let's first loook at atavisms. We have brought a few into discussion already. Atavistic legs on whales. Two extra toes on horses. Unfused leg bones in horses. Atavistic tails on humans. The observation is that these atavisms ONLY manifest themselves in a pattern consistent with the phylogenic trees generated from the other lines of evidence. The atavisms only make parts that were possessed by their ancestors in the common descent interpretation. You never see atavisms that fail to follow this pattern. Common descent offers a simple explanation. The common designer option gives no reason why we should expect whales to have genes for making legs of humans to have genes for making tails. They are again forced into capricious explanations.
Development tells a similar story.This has the potential to get rather complicated, so I'll stick with an example already in play. We observe that whales go through a developmental stage in which they possess rear legs. Again, this shared developmental trait follows the same pattern as the other lines of evidence. Common descent offers a simple reason for this to be the case. A common designer has no logical reason to send whales through a stage with legs which must later be reabsorbed.
This can keep going for a long time. If you look at other areas of evidence, you keep coming back to the observation that all the bits always fit the tree that you get from morphology and genetics. This is true for parahomlogy. This is true for vestiges. This is true for the chronology of the fossils. Every observation that you make brings you back to these same trees.
So the question is which interpretation of the data fits the observations. The answer is that common descent offers a simple and compelling answer for each one. A common designer can be hypothesized for some of the observations but for many of the observations, the evidence is the opposite of what would be expected. The only recourse for YEers is to ignore these contradictions. BUt you really must worry about someone's ideas when they must ignore so much.