I just posted on how not to argue against evolution. I want to add a brief word now on how to argue against it. I’m not trying to make this comprehensive, just to list a few quick points covering categories that count against evolution. (I’m still speaking strictly of naturalistic evolution.)
Can’t you just see by looking that this world is designed?
This objection will suffer snickers from evolutionary scientists, because it lacks testability and definitional rigor. It’s unscientific, they say (rightly), to draw such a sweeping conclusion unless we have (for example) an undesigned world and a designed world next to each other so we can compare their broad features.
There is, however, knowledge other than scientific knowledge, and we really can see design in all of reality. It takes a strong contrary metaphysical view to deny it. It’s not science that denies design, it’s persons’ philosophies.
Evolutionists will also object that some of reality looks undesigned: that there are apparent mistakes, evil, and so on. Still it takes some sense of the reality of design to detect anomalies in it.
We know from Scripture that God created the world, including all of its life.
This is valid—even if evolutionists laugh at it—as long as we establish that God’s revelation is a genuine source of knowledge. To explain the many ways we can do that would fill more than a book, but it can be done.
Once we know that God is Creator, we know that naturalistic evolution—the theory that everything came to be by unguided natural processes—simply can’t be true. We can go on from there to discuss exactly what it is that Scripture teaches about creation, its days and its order and so on, though I strongly advise humility on that point. Regardless of those controversies, clearly God has ruled over nature from the beginning.
Naturalism is false, therefore naturalistic evolution is false.
Naturalistic evolution is joined at the hip with philosophical naturalism, the view that nothing exists but matter and energy interacting according to law (necessity) and chance. If you know how to argue (philosophically) against this naturalism, you can extend the argument to count against naturalistic evolution as well.
Finally: Know what you’re talking about.
For those who want to dig into the discussions deeper than this, digging in deeper is exactly what you need to do. Learn evolutionary theory. Learn it well—as well as you can, given your educational background and opportunities. Study it from the evolutionists’ sources. Study contrary views, too, but don’t base your knowledge of evolution on creationists or Intelligent Design proponents. Learn its best arguments from its best proponents. If you can still mount an argument against naturalistic evolution after that—and I think you can—it will be a strong one.
The same goes for the philosophical discussions on naturalism, and for explaining how we can trust Scripture as a source of knowledge: dig in! You’ll be well rewarded by your efforts.
P.S.: An important follow-up: Why (and Why Not) Argue Against Evolution