Just like any other creature, a chariot can only suffer a certain number of wounds before it is destroyed. Roll to wound as normal, and take any saves that apply as explained below. A chariot has a pool of Wounds which represent the chariot itself, its crew and the creatures pulling it. When a chariot loses its last Wound, remove the whole model from the battlefield.
If a chariot is hit and wounded by an attack which is of Strength 7 or more, it is destroyed automatically with no armour saving throw allowed - even the most strongest chariot can be blown apart if hit by a cannonball!
If a chariot is destroyed, all of its crew are automatically killed. Any characters in the chariot (see below) will suffer a single S5 hit if it is destroyed. If they survive, they may continue to fight on foot. Survivors are placed within 2" of the place where the chariot was. If the chariot was in close combat before it was destroyed, any surviving characters will continue the fight on foot.