When you want to fire against a chariot, treat it like any other unit. Roll to hit and to wound against the chariot in the same way as against troops. Any hits scored are targeted towards the chariot as a whole, unless any characters are riding in the chariot (see Characters & Chariots). Some chariots are large targets and you therefore get a +1 to hit bonus when shooting at them. If the chariot is a large target, this is clearly indicated in its army list entry.
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.