Do we know how matter moves matter? I was surprised when reading an apologetics book recently that attempted a rebuttal of the claim that "An immaterial mind cannot interact with the physical order." Here was the response:

How could a spiritual entity interact with the physical order? How could a god, an immaterial mind, affect or move matter? If mind cannot interact with matter, then a supernatural entity cannot create a natural or physical world.
Admittedly, we have no idea how mind can move matter. But how big a problem is this? It could be monumental if it were not for one thing: in the end, we have no idea how matter moves matter. Despite what is sometimes said, we do not actually experience physical causality in any deep way. We see that matter moves matter in some sense, but we do not see why or how it happens. We see someone throw a pencil across the room: we can see the hand grasp the pencil, we can see the arm move back, and we cna see the pencil leave the hand and fly across the room. We do not, however, see the causation. Hume was right on this point: all we have are laws associating causes with effects.

Is this an accurate statement? I'm hoping that this is more of a physics question than a philosophical one. Perhaps the answer is as simple as to whether we understand how matter moves matter. Though, I'll grant that I can't tell if they are using "moves" in the billiard ball striking sense or in the sense of some philosophical first cause sense. All of their examples use a human choosing to do something rather than just discussing whether we know how a moving billiard ball moves one it strikes.
 A: From a physicist's point of view the quote is nonsense: gravity and electrodynamics are how matter moves matter on the macroscopic scale and we have perfectly good theories for both of them.
If the writer means "we don't actually know how it really works when you get right down to it; I mean not really know." then he's speaking pure, unadulterated philosophy.
Now, when I see a quote full of phases like "do not actually experience physical causality in any deep way." (emphasis added) it suggests to me that we're talking philosophy here; which is fine, but if the writer does not accept that physics can---even in principle---answer his question than it is not a scientific question.
A: Philosophers (some of them) get "wrapped around the axle" with questions like this because they are impoverished in ways of thinking about things.
Like if they ask "how could an immaterial thing influence the physical world" they really have no concept of information.
One program could drive a robot to mix a drink; another could drive it to pull a trigger.
In fact, there could be a "bit", a 0 or 1, in it's working storage, that chooses which it will do.
The bit is just the state of something that has two possibilities, like a light switch, which is "up" or "down".
Information is not a material thing.
What it is is an arrangement of material things.
A similar question might be - suppose I see a candle flame.
Is that a material thing, or not?
You could say it's just behavior of something, not actually something of it's own.
It's just arranged in a state of having information that determines how it behaves.
These concepts of "immateriality" (I'm not touching "spiritual") are the kinds of impoverished models some of us are limited to.
I got most of my understanding of these issues during my PhD work under Marvin Minsky.
I would encourage you to read some of his stuff.
It's fascinating.
A: Although you wanted the physics question, I think it is important to answer the philosophical question. The question is: how can my own immaterial soul move my hand and body, when my hand and body are material?
The obvious answer is that the immaterial soul is attached to a material object, namely the brain, and it is some sort of high-level description of the enormous amount of computation going on in the brain. Computation is not a material object, but an abstract verb acting on data which is an abstract noun. It is equally abstract whether it is going on in a brain or in a computer. But in the case of a computer, you know exactly what is going on, so I'll just think about that. It is manifestly obvious to me that the computer is a good model of the brain, this was convincingly argued by Turing, but within philosophy, this is still a debate, which is why you can basically ignore philosophers. Their field is intellectually bankrupt, most likely because they have no arbiter of truth other than political persuasion: they have no theorems and they have no experiments. You can't make progress with pure politics. Historically, this method fails to produce true answers about questions as simple and obvious as "does the Earth rotate?"
The microsoft Windows operating system is just as abstract as a soul. It's an immaterial pattern, a collection of bits, which is realized in CDs, in computer RAM, in static RAM, or in magnetic drives. The windows soul is the same even if the substrate changes.
When you talk about cause and effect, you are always talking at a very high level. I don't know what the colloquial notion of "cause" and "effect" mean exactly in physical terms. They only have meaning in a computational sense. When you have a program running a factoring program, and you feed it 65537, you can ask what causes it to run through all possibilities without finding anything? The answer is that 65537 is prime. If you ask "why is 65537 prime?" the answer is because the program runs through all the possibilities! The notion of cause and effect is nonsense, it's not fundamental to physics, and it probably doesn't exist. It's a shorthand for "what can I change in order to have an impact in the world", and in this way of thinking, causality, as in X causes Y, is best formulated as "If I tell you I do X, is Y likely to happen?"
The notion that something abstract can interfere with the universe is either tautologically absurd or manifestly obvious. The properties of material objects will continue independent of any abstract realm considerations, so there is no way some agent outside of nature can change those things. But if there is a complex computation going on, the properties of these complex computations are revealed over time. So you can say "The primeness of 65537 made my program run through all the possible factors without finding anything". Somebody could then ask "how could the primeness of a number influence the physical world?" And the answer in this case is because this part of the physical world was computing something that depended on this property.
So if you view the abstract realm properly, it doesn't physically alter the stuff that happens to us, but it can provide a framework for qualities which are not apparent which explain the outcome of certain complex computations. If you formulate "abstract property A causes physical consequence X in system S" as "System S is implementing a computation where abstract property A implies consequence X", and then it is not mysterious how abstract properties can influence the physical world.
But some people say Jehovah came down and parted the red sea in a literal sense. This is mentally deranged.
