The first and most noticeable sign is that your battery goes dead.
If you have a stereo or other equipment and you find your alternator charges better when it's cold or charging falls off as the alternator heats up. This is a sure sign that your alternators bridge rectifier is going bad. The bridge rectifier had diodes that are affected by heat.
Always wear safety glasses when working around your alternator or battery. I have seen several batteries explode in my life time. So many times in my lifetime I've had something bounce of my safety lenses and thought, "I'm sure glad I had safety glasses on, or I would have lost an eye!"
When working on electrical where you need to disconnect the power be sure to disconnect the negative power cable. If you disconnect the ground your positive will be dead as well. Disconnecting the ground is better than the positive because the positive can short with lots of sparks if you ground the terminal as your taking it off.
Your alternator should charge at about 14.5 volts 15v is OK but by the time you get to about 16 volts you will start to blow light bulbs.
A bad battery may make it so your alternator will not come up to the proper voltage. If your vehicle won't start charge your battery and see if it starts.
When your bridge rectifier goes bad it can also drain your battery. If you have a situation where your battery keeps gong dead overnight try disconnecting the battery wire from the back of the alternator. If the diodes in the bridge rectifier short out they will drain your battery. If you disconnect the battery wire from the back of your and your battery no longer goes dead then you need to replace your bridge rectifier or replace your complete alternator.
If you must jack up the vehicle to work under it, be sure to put something under the vehicle in case it falls. I always us as many safety devices as possible. Quite often I will use two jack stands and the jack. Also, if I have the tire off I will throw them under the vehicle as well. In the past 6 months I have read at least two articles where someone took the tires off there car, jacked it up, got under it and it fell on them. Why didn't they at least put the tires under the vehicle. I'm not going to use the derogatory terms like Idiot, moron, stupid, you can insert them yourself.