My favorite clear-cut example of how order appears without intelligent direction is (big surprise) geological.
- Take a bag of mud sand and gravel all stirred up and mixed in a disordered fashion.
- Pour that bag into a tall container, like a graduated cylinder.
- As you will quickly see, the gravel falls first, followed by the sand and finally the mud settles out.
- When all of the sediment has settled, you will have several well-ordered layers of sediment. You have done nothing to put them in order. It was done by natural processes.
- We see exactly this same process occurring in nature. Sediment sizes tell us a lot about how they were deposited.
- None of this requires any sort of intervention.
This is a simple example that can be easily demonstrated. There are countless more complex examples that can be demonstrated with a little (or a lot) more effort.
Now if you want to discover how things can become ordered in a closed system while the disorder (entropy) of the universe is increasing overall, that will require some study of physics. But as an analogy, think of how you can increase the warmth in closed systems, like houses, by lighting a fire, even if the temperature outside is dropping.