Use a digital multimeter. Place leads across the battery posts, everything off. The generic spec for a full charge is around 12.6 volts. If the battery is down, take it off and get it charged. Cant do much testing if the battery is down. Then start vehicle, take same reading across the battery posts, again. The second reading should be higher than 12.6volts if charging system is working. If not charging, There could be a wiring problem to or from the alternator?