When damage is dealt to a unit (either through combat or a special ability) the controller of that unit must then assign the damage to the figures on the base. Lethal damage must first be assigned to the figure on the unit with the most (or tied for the most) nonlethal damage on it. Lethal damage means that a figure has damage on it equal to or greater than its hit points. Usually only one figure on a unit will have damage on it at a time. However, in the event that two figures have damage on them, the one with the most damage on it must be assigned lethal damage first. If two figures are tied for most damage, the controller of the unit chooses which one to assign damage to.
Once all damage is assigned, it is all dealt simultaneously. Figures are downed as soon as they have lethal damage on them (damage equal to or greater than their hit points). Remove downed figures from the battlefield. A unit is defeated when it has no figures. Remove a defeated unit from the battlefield. This is true of both combat and non-combat damage-- all damage must be assigned using the same rules, and damage is dealt simultaneously. Each figure dealt lethal damage is downed simultaneously. (For example, if a special ability deals 3 damage to a unit, all 3 damage is assigned and then dealt simultaneously.)
If a unit takes damage and assigns that damage to a figure with multiple hit points, but not enough damage to down that figure, the damage stays on that figure until the end of the turn. Place a die next to that unit with a number representing how much damage is on that figure. Figures with damage on them are considered injured. That damage is on the figure, not the slot, so if the figure is later repositioned into a different slot the damage moves with it. At the end of each turn, all damage is removed from figures.
All damage has a source. In the case of combat damage the damage is coming from the unit that rolled the dice. Some special abilities will describe their source. If a source of damage from a special ability is unclear, however, it is considered to be coming from the unit with the special ability. Most damage is dealt by units, but if a figure deals damage the source is considered the unit that figure is on. If the source of damage leaves the battlefield before damage is dealt (for example, a special ability that requires downing the unit as an additional cost) the source is still that unit.
If a unit is destroyed, each figure in that unit is considered to have been downed. Any special ability that triggers when a figure is downed will trigger if the unit itself is destroyed, such as by a special ability.