The heavens declare the glory of God,/In essence this is straightforward. In everyday life it is apparent that many things are designed by men. We recognise design. And we know that designed objects have a designer. The parallel is that we see many other things that are not designed by men but are clearly designed.
and the sky above proclaims his handiwork. (Psalm 19:1)
We recognise design by purpose or intent. While a splatter painting may have been drawn by an artist there is no clear intent so whether or no it was designed is not clearly apparent. However the more intent something has the more clearly it was designed.
Information content is a helpful way of assessing design. The higher the information content the more obvious it is designed. Information is based on specification and complexity. So if something is ordered it is not particularly complex. If something is complex based on the number of bits to store it, it is may or may not be specified. So storing 100 addresses is specific, 100 random letters is not. A measure of information can be made by the the storage capacity required to hold the generator of the data. For a story it is the data (ie. every single letter, though thru lossless compression it may be possible to minimise information content) as a story is specified and not predictable. However large quantity data that is predictable (⅓ in decimal), calculable (π, e) or random has a low information content.
The issue with random numbers or noise needs more explanation. It is low information because describing a random number generator requires little information. To describe any single random number will require as much data as an equivalent length story. The reason this is not high information is that it lacks any specificity. The binary data that describes a jpeg picture may appear random but it is specific, it stores data about a specific object.
People don't perform these calculations rigorously but as information content ranges over multiple orders of magnitude design is easily recognised. A smoothed rock is easily distinguishable from a carving. We can tell a painting from spilled paint (usually). We know that a book has an author.
So it is clear that design can be seen even if the designer is not known. The existence of a designer can be inferred from design. So when one sees all the design in this world that is not from the hands of man the logical conclusion is that a designer exists and he is other than man. One may claim this designer is other than the Grand Designer; whether that be an angel, a lesser god of a pantheon, an extraterrestrial being. But whatever the immediate source, these beings are still creatures and the ultimate source must be the Creator.