If your battery is dead, keeps running down or cranks your engine slowly, you may have a charging problem. Likewise, if the alternator or battery warning light is on, or the amp or voltage gauge is reading low, that too probably indicates a charging problem.
A quick way to check the charging system is to start the car and turn on the headlights. If the headlights are dim, it indicates the lights are running off the battery and that little or no juice is being produced by the alternator. If the lights get brighter as you rev the engine, it means the alternator is producing some current but may not be producing enough at idle to keep the battery properly charged. If the lights have normal brightness and don't change intensity as the engine is revved, your charging system is functioning normally.
You can also check the charging system by connecting the leads of a voltmeter to the battery. When the engine starts, the charging voltage should jump to about 14.5 or higher. If the reading doesn't change or rises less than a volt, you have a charging problem that will require further diagnosis.
Alternators are pretty rugged, but can succumb to excessive heat and overwork. They can also be damaged by sudden voltage overloads (as when someone attempts to jump start a dead battery and crosses up the jumper connections or if someone disconnects a battery cable from the battery while the engine is running).
Sometimes alternators can partially fail. In the back of every alternator is a "diode trio" that converts the alternators AC (alternating current) output to DC (direct current). If one or more of these diodes fail, the alternator's amperage output will be reduced. It may continue to produce some current, but not enough to keep the battery fully charged -- especially at idle or low speed.
Most service facilities have test equipment that can identify these kind of problems. So if you suspect a weak alternator, you should have it tested to see if it needs replacing.
Most service facilities do not repair or rebuild alternators because it's too time consuming and requires special parts. Most will replace your old unit with a new or remanufactured unit. Your old alternator is usually traded in or exchanged for a credit (so it can be remanufactured and sold to someone else).
CAUTION: If you're replacing an alternator yourself, always disconnect the battery before unhooking the wiring on the alternator. This step will eliminate the possibility of accidentally shorting out a hot ware and damaging something or starting a fire.
The alternator drive belt should be inspected at this time, and replaced if it is cracked, oil soaked, glazed, badly worn or otherwise damaged. The belt should be adjusted for proper tension following the vehicle manufacturer's guidelines. Too much tension can overload the alternator's bearings and shorten the unit's life (as well as belt life), while too little tension may allow the belt to slip.