This can range from generalized philosophical argument, that the universe in its form and beauty looks more like the work of intelligence that blind chance. But obviously that isn't enough, except as a starting place.
It can also involve particular arguments. For instance, a Darwinist would argue that animals with eyes have a survival advantage over animals without eyes. But how do you explain how the eye gradually evolved over numerous generations, and apparently did so several times among different orders, when only a developed eye would be of any use? Not a fully developed eye, necessarily, but one developed enough actually to see things.
Or, how do you explain the development of wings? If they developed gradually, partial wings would actually be an encumbrance, until they had developed to the point where they would be useful. It's not enough to suggest that full-flight wings developed from gliding creatures, because you still run into the same basic problem of what advantage the progenitors of these gliding creatures had before their wings were developed enough to be useful. Before that, they still would have been encumbrances, something to get tangled up in the bushes while fleeing from predators.
But the main argument has been on the micro level, involving statistical analysis, as anyone knows who has read up on the subject. These arguments are detailed and persuasive.
"What test can you postulate that would allow us to demonstrate the function of Intelligent design? How do I look at a subject and objectively prove that it "looks more like" intelligent design?"
A good starting point might basic common sense. Look at the shirt you are wearing. Can you tell that it was intelligently designed and manufactured? How can you tell that?
OK, so that's not quite a fair question because we know that people manufacture shirts. So let's take another example. Suppose you were walking along the beach and you see the words "E = MC^2" written in large letters in the sand. How would you go about determining if it appeared by random chance with no intelligence?
I am constantly amazed the baloney evolutionists use to try to discredit the theory of Intelligent Design. Can't be falsified? Then I suppose my theory that the words on the beach were written by an intelligent being can't be falsified either.
In a sense it can't. Unless I can show a video of a person actually writing the letters, how can I "prove" that the message wasn't a result of random wind effects? I can't. That is the kind of ridiculous standard evolutionist require for ID.