Use an inexpensive digital voltmeter to measure the battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. If it's low, suspect the generator. If it's okay, the battery is defective or there's a drain on it when the ignition switch is off. There is a special procedure now for checking for a draw because some computers will draw a high current until they go to "sleep mode" in up to 20 minutes.
Be aware GM's generator is the worst design in the world, and it's very common to go through four to six of them in the life of the vehicle. What many professionals have found out is to reduce the repeat failures, replace the battery at the same time unless it's less than about two years old. Due to their design, these generators develop huge voltage spikes. As the battery ages, it loses its ability to dampen and absorb those spikes. They can destroy the internal diodes and voltage regulator inside the generator, hence, the repeat failures. The old battery will work fine in a 1986 or older vehicle that has the really good design generator.