Start the car and then remove the negative battery cable. If the car dies, then the alternator is not putting out enough charge.
To test the battery, check the voltage with the engine off, a fully charged battery should read over 12.5 volts. Then disconnect the center coil wire from the distributor so you can crank the engine without starting it. Crank it for 10 - 20 seconds, If the voltage drops below 10 Volts while cranking your engine over, then your battery is bad and not holding enough charge...