An activated alternator or battery light means more electricity is being used than is being replaced. The good news is with this mechanic frequently asked question—it's probably not fatal—just massively inconvenient. The rule is to keep driving until you reach a service station. Turn off as many electricity-draining accessories as you safely can. The hardest thing the electrical system has to do is start the car, so don't turn the engine off unless it's absolutely necessary.
Warning! If the temperature light comes on at the same time the alternator light is on (or simply by itself), stop the car as soon as you can. The same belt that drives the alternator often drives the water pump. If the water pump stops working, it won't be long before the engine overheats and its internal parts melt. The result will be major damage and expensive repairs.