Just a note regarding the starter and alternator tests, the on car tests are actualy more valid as the bench tests have no significant loads (be it engine compression for a starter or electrical loads for the alternator) and its under such conditions that the faults will be visable.
As an overview of an alternator and how it works, consider the following.
A basic alternator (e.g. not a modern ECU controlled unit) consists of a stationary part (stator) and a rotating part (rotor), rectifier, regulator and as the name suggests, it produces an alternating current (AC) and not a direct current (DC).
This current is produced by exiting a coil on the rotor to produce a magnetic field, as this magnetic field rotates, it induces a current in a set of windings in the stator.
The stator will have at least three windings (usualy many more!) and produces three phase AC.
To turn this AC into DC to charge a battery it is fed into a rectifier (often refered to as a bridge rectifier or bridge), this is made up of 6 diodes which rectify the AC into DC.
So, thats the basics, there are a few more bits to consider.
Voltage regulation, if not controlled the output voltage will increase to high levels as the rotor speed goes up and/or the electrical load reduces, to combat this, a regulator is fitted.
This device controls the amount of current that is fed to the rotor winding via the slip rings and brushes and hence it is possible to vary the magnetic field in the rotor. This consequently varies the stator currrent and therefore the output voltage. The regulator measures the output voltage and automaticaly limits it to a preset value (this can be upto 14.6V for a calcium battery based system and can be seen with little electrical load and a charged battery).
The dash lamp does have a main use to. The basic alternator regulators do NOT take the power for the field from the battery (or they the rotor filed would be permanently energised with the igniton off and drain the battery), they get it from the dash lamp and an additional small rectifier.
So when you start the car, the ignition provides battery positive to one side of the lamp, the other side is connected to the regulator, this gives the regulator a feed to initilaise the field winding on the rotor (this explains why the bulbs used for the charge indicator are normaly quite a few watts). As the rotor starts to spin, the stator windings produce an output current, this is rectified by the additional small rectifier which feeds the resulting volts to the regulator on the lamp side. The bulb now goes out as it has positive volts on both sides and the regulator now has an alterntive power source from the alternator
So possible issues.
Regulator failure - These normaly fail short circuit and hence the output volts go way beyond the max volts as there is no control present, note the dash lamp will extinguish in this case. If they go open circuit then dash lamp will remain on.
Rectifier failure - Normaly spotted by reports of poor charging and a slightly flickering dash lamp. This is because only one of the diodes generaly fails at a time so the alternator still outputs current but it is reduced.
Dash bulb failure - will stop the alternator working altogether.
Bearing failure - Results in noise
Brush wear - Very rare these days although the awful old top mounted brush system as used by lucas in the 70's/80's does suffer this. Symptoms would be no charging and dashlight iluminated.
As an aside, those who have ever stripped an alternator may have noticed that the iron sections of the rotor are triangular in shape, this is by design and is done so that the AC output is not a true sinusoid and is more 'flat topped' with steeper edges. This gives the result of an electricaly quieter alternator with less 'ripple' on the output.
Dont be afraid of alternators, they are simple and pretty easy to repair.