Rules as Written, you may split your dice pool when firing two Pistol or SMG-class weapons with a single action (SR4A), when attacking multiple targets in melee with a single weapon & action (SR4A), when casting multiple spells with a single action (SR4A), and when attacking with multiple melee weapons with a single action (Ars). I believe there was also an instance in hacking where you could split your dice pool, but cannot recall what/where.
In all instances, splitting your dice pool involves using a single action to take multiple actions of the same type. As far as I can remember, there is no overarching rule for this, although it is implied.
In all locations except casting multiple spells, it instructs you to divide your base Dice Pool, then apply modifiers (Positive & Negative) to each resulting pool separately. The FAQ instructs you to do this with casting multiple spells as well - something that was heavily implied but not actually stated in RAW. The disconnect between the FAQ & RAW comes in what is defined as a Dice Pool Modifier.
RAW specifically states that a dice pool consists of (Attribute) + (Skill) + (Modifiers), exceptions being attribute-only tests, which simply replace Skill with another attribute or remove it entirely, or some matrix tests, which substitute a program for an attribute. Thus, anything that does not directly increase the Attribute or Skill being used, but does increase the dice pool, is a dice pool modifier. Whereas the FAQ includes focus' & (I think) specialization as part of the base pool for some random reason.