Some theories on how God acts in the world. Are any necessarily incompatible with Orthodoxy?
1. Deism: God created matter in the very beginning, and gave matter certain properties such that matter acted according to well-defined natural laws, such that the universe can now develop without the direct interference of God. Anything seemingly miraculous is due to God-given natural laws we humans haven't yet recognized.
2. Radical theism (or "occasionalism"): Everything that happens, is due to God's direct action, not due to a natural cause. The sun does not cause water to evaporate. God causes the water to evaporate. The observation that when the sun shines on water, the sun causes water to evaporate, is due to humans mistakenly thinking that "x causes y", when actually "God causes x" and "God causes y". God causes the sun's existence, and God causes the sun to shine on water, and God causes the water to evaporate.
3. Via Secondary Causes: God is the primary cause (or "direct cause") of the mere existence of nature, but God acts through nature in order to fulfill his will. These acts of nature, or secondary causes, make up the web of cause-and-effect in the natural world. Secondary causes are natural causes. If God wants water to evaporate, then God would act through the sun as a natural cause, rather than directly causing water to evaporate.
4. Via Persuasion: God "persuades" nature to act in ways consistent with his will, but he can't force nature to act thus. This fact would explain why natural disasters (killing hundreds or thousands of people) exist: God is good, but God can only persuade nature to act in certain ways. Likewise, God can only persuade humans to act in Godly ways (thus accounting for human evil, while maintaining God's goodness). God persuades nature towards greater and greater levels of "enjoyment".
5. Via Quantum "Randomness": God acts at the quantum level. At the level of electrons, photons, and quarks, there is a degree of unpredictability. If photons traveling through space could hit position A, B, or C, and if quantum theory can predict that the photons, on average, will hit B 80% of the time; A, 10%; and C, 10%, then God acts in determining how exactly that percentage is achieved.
For instance, let's say in one experiment that the first photon hits B, and the second photon hits C, and so on, until 80% hit B, and 10% each hit both A and C individually. In another experiment, the first photon hits C, and the second hits A, and so on, until the 10%/80%/10% distribution is achieved. Both experiments are consistent with the predictions of quantum theory, but what determines which photon goes precisely where? Why did the first photon in one experiment hit B, and in another experiment, the first photon hits C? Quantum theory can't explain that particular observation, and it is at this level that God can act. In other words, God can be the reason behind the different actions of the first photons. God's action thus does not violate the laws of physics, but his action does affect the world.
6. Mind-Body model: God acts on the world like a human mind acts on the human body. One's mind directs and controls the body, by using the body's chemistry, organs, and limbs. Likewise, God is the Great Mind, and the universe is his body. God's consciousness permeates the universe (like our consciousness of sensations permeates our body, thanks to nerve cells).
7. Information-Source: God acts like a choir director in relationship to a choir. God is the source of "information" on which the choir acts. The choir has a definite interest in following the information given by the choir director, and its voices are tuned accordingly.
(Alister McGrath, Science and Religion: A New Introduction, gives a nice summary of these positions.)