Go out and get a multimeter, like the one below at Harbor Freight tools. Check the battery with the car off. Should be between 12 to 13 volts. Then start the car, and test again. If it now reads more, like 14volts, then your alternator is charging the battery. If its the same, check to make sure the wiring is not at fault. To do that, put the positive lead of the multimeter to the positive side of the alternator. Put the black/ground wire of the multimeter to the block, or a ground somewhere on the car. If the alternator does not read any better than the battery, then its bad. If its reading higher, like 14 volts or so, then it could be the wires or voltage regulator. There are alot of videos on the internet that shows this.
Digital Multimeter - Save on this 7 Function Digital Multimeter
Digital Multimeter - Save on this 7 Function Digital Multimeter