Evolutionary argument against naturalism
The evolutionary argument against naturalism is an argument advanced by Alvin Plantinga to show that metaphysical naturalism contains its own "defeater": if our beliefs are a result solely of natural processes, then they are unreliable. Thus, the belief that only nature exists is itself suspect.
In brief, Plantinga argues that natural selection affects mental processes, not just physical characteristics. However, natural selection does not select for truth, only usefulness. That is, if a false belief helps an animal survive better than a true belief, then selection will favor the false belief. Therefore there is no guarantee that any belief belief we hold is true.
This applies to belief in naturalism itself: a naturalist believes that his thought processes are the result of natural processes, which produce unreliable beliefs. And therefore, belief in naturalism is unreliable.
Reasons why evolution favors some reliable faculties
Plantinga's argument seems to favor an unjustifiably simplistic view of instinct. Certain learning behaviors appear to be instinctual, such as the drives to acquire language, to connect socially with certain other individuals, to investigate novel objects and places, and to hear and tell stories. Evolution has good reason to select for individuals with an accurate understanding of (at least some parts) of the world because this is the most economical and foolproof way to ensure survival and reproduction. For example, in the tiger example, it would be possible for a person to be ambivalent about being eaten, or even desire it, but to have instincts that cause him to run away. However, this would require a different set of instincts for each sort of threat, and/or a complex justification to arise that would cause him to usually act so as to avoid death, even if he doesn't mind dying.
In contrast, giving a human being a sense of pain, a general desire to avoid injury, and an accurate understanding of what might cause injury, is in fact a much simpler and more effective solution. It is less likely to malfunction in unusual circumstances and requires less complexity and power in the brain. Just a few instincts could account for almost all survival situations. One would expect, therefore, that evolution would be far more likely to select for individuals who try to behave according to a roughly accurate understanding of their world and useful goals, than individuals with a large and unwieldy set of instincts designed to elicit just the right behavior in every circumstance. The latter solution is too vulnerable and too unnecessarily complex to be favored.
One final way to drive the point home would be to parody the argument this way: why, when a tiger runs towards a man, does he see the tiger and run from it? Why does he not instead hear a friend calling from the opposite direction and run for that reason? This situation is analogous, because accurate perception through hearing and vision are also complex, evolutionarily selected traits, but both can only be selected for due to the behaviors they elicit. By Plantinga's argument both solutions should be possible evolutionary adaptations. But though both of these possible tiger-aversion strategies would accomplish the same goal, only one could be reasonably expected to evolve, because the other would require the evolution of a far more complex, less generalizable, and easily confused faculty to accomplish the same objective.
While having a sufficiently advanced cognitive apparatus to survive in prehistoric times does not imply having a sufficiently advanced cognitive apparatus to fully understand the world, there's no clear reason why parts of the brain which evolved to possess skills necessary for survival and social interaction should not be able to accurately understand other phenomena which require similar skills.
Furthermore, evolution can account for traits of the human mind that are not well designed to accurately model the world, such as certain forms of superstition, anxiety disorders, inflated self-esteem, and optical illusions. It also provides at least a rough explanation for why human beings are not good at certain types of thought and information processing and are prone to logical fallacies and cognitive bias. Creationism or intelligent design cannot adequately explain these features of the human mind, nor generally predict other areas in which human beings may be prone to error.
Beliefs interact with each other
Our beliefs do not exist in isolation, but rather reinforce or contradict each other. One cannot, for instance, rationally believe that playing the lottery is a waste of money, and also that playing the lottery is a good long-term investment.
If one is unsure about a belief, one can try to find ways to corroborate or disprove it. If someone senses someone walking around outside their house, they can listen for footsteps, and go look for footprints. Each of these beliefs ("I had a sensation of someone walking around", "I thought I heard/didn't hear footsteps", and "I thought I saw/didn't see footprints"), in isolation, could be wrong. However, if all three point in the same direction (either there was a feeling, and footsteps, and footprints; or no feeling, no sound, and no footprints), then the conclusion becomes more reliable.
In fact, science is a method for finding out which of our beliefs are true.
It is possible to imagine scenarios in which a person holds two or more erroneous beliefs that do not contradict each other, leading that person to a false conclusion. Most of these, however, are either obviously ambiguous, or contrived.