How do computers work (see details)?

I know about the CPU, RAM, ROM, hard drive, etc. I know about programs. I also know about transisters, logic gates, logic circuits, etc. But what I am having trouble understanding is how, given instructions, the CPU changes its fuction, like changing from adding numbers, to dividing, to whatever else it does. So, basicly, I am asking how higher function arises out of the basic logic circuits of a computer.