As a further insight to the nature of my confusion, here's how I think a ranged attack (maybe with a handgun of some kind) should go:
1) Form a dice pool for, say, an AGI attribute test. The character gets 3D6 for the attribute, 2D6 for skill with the gun, and 1D6 for the weapon itself, totalling 6D6. Let's say this matches his maximum pool and there are no deductions for range, cover, etc.
2) (Confusion here because I may not yet have read the appropriate section of the rule book) The GM sets a difficulty level of 13 to hit (does he? or is there some other way of determining what score is needed to hit?).
3) The character decides to use, say, 4D6 to see if he hits which gives him just over a 50% chance of success, retaining (spending?) 2D6 to provide 1D6 of extra damage. If the attack fails (scores less than 13) the other 2D6 are not used because no damage is done.
I have no idea if I have interpreted the rules correctly but that seems to me to be what is suggested by the rule book. I am sure that, ultimately, I shall see I am just being dense but, right now, I have no idea if I am way off or close to understanding. At least this way, more experienced characters will have more dice to play with in combat.