The fundamental claim of intelligent design is straightforward and easily intelligible: namely, there are natural systems that cannot be adequately explained in terms of undirected natural forces and that exhibit features which in any other circumstance we would attribute to intelligence.
Regardless of one's point of view, it's quite easy to see that Darwinism is not in the same league as the hard sciences. For instance, Darwinists will often compare their theory favorably to Einsteinian physics, claiming that Darwinism is just as well established as general relativity. Yet how many physicists, while arguing for the truth of Einsteinian physics, will claim that general relativity is as well established as Darwin’s theory? Zero.
Whenever explaining an event, we must choose from three competing modes of explanation. These are regularity, chance, and design... To attribute an event to design is to say that it cannot reasonably be referred to either regularity or chance.
The very comprehensibility of the world points to an intelligence behind the world. Indeed, science would be impossible if our intelligence were not adapted to the intelligibility of the world. The match between our intelligence and the intelligibility of the world is no accident. Nor can it properly be attributed to natural selection, which places a premium on survival and reproduction and has no stake in truth or conscious thought. Indeed, meat-puppet robots are just fine as the output of a Darwinian evolutionary process.
Constrained optimization is the art of compromise between conflicting objectives. This is what design is all about. To find fault with biological design - as Stephen Jay Gould regularly does - because it misses some idealized optimum is therefore gratuitous. Not knowing the objectives of the designer, Gould is in no position to say whether the designer has proposed a faulty compromise among those objectives.
Even if the intelligent design of some structure has been established, it still is a separate question whether a wise, powerful, and beneficent God ought to have designed a complex, information-rich structure one way or another. For the sake of argument, let's grant that certain designed structures are not simply, as Gould put it, "odd" or "funny," but even cruel. What of it? Philosophical theology has abundant resources for dealing with the problem of evil, maintaining a God who is both omnipotent and benevolent in the face of evil.
Naturalism is the view that the physical world is a self-contained system that works by blind, unbroken natural laws. Naturalism doesn't come right out and say there's nothing beyond nature. Rather, it says that nothing beyond nature could have any conceivable relevance to what happens in nature. Naturalism's answer to theism is not atheism but benign neglect. People are welcome to believe in God, though not a God who makes a difference in the natural order.