C and D are plain log scales, where one decade is the length of the rule. They're sort of the default scales to use.
Multiplication is commutative, so you put either number on either scale. The important thing is that the distance from the left index of the scale is proportional to the log of the number (reading the scale as 1 to 10), so you want to arrange the scales to add the lengths corresponding to your numbers such that the lengths add up. (Or so that you subtract the length of the divisor from the dividend, if you're dividing).
You can get by without the approximation if you're willing to set up the multiplication, see that the product is out there in thin air, then move the slide to put the right index where you originally put the left index. (3 times 5: on the d scale find 3 and put the left index of the C scale there; opposite 5 on the C scale read nothing because there's no D scale there; try again using the right index of the C scale, which is the same thing as having another copy of the D scale out there to the right where the air was).
A and B are each 2 copies of a log scale. You can absolutely use the left side of A and B for your numbers to multiply, and the product will always be on the scale.
People normally use(d?) C and D because the precision is better and because the rest of the scales (like the trig and log-log) are constructed to work with them.