First thing is to check the Battery, see my post here.
Provided your battery is good, the following will let you know about the alternator.
Start the vehicle and let it idle. The voltage should be about 2 volts above open circuit voltage.
You can also do a loaded voltage output test. Turn on the high beam headlamps, AC on high, rear defogger etc. Bring the engine RPM up to 2000 RPM and check the voltage at the battery. It should be at least 0.5 volts above open circuit voltage.
You also need to check for AC ripple to make sure the diode rectifiers are still good. Put you meter on AC volts put the black lead on the battery ground and the red lead on the output lead of the alternator. You shouldn't have more than 0.5 AC volts, if you do the alternator is bad.
Most auto parts stores in the USA will check you battery and alternator for free. No idea what's available in Russia but it's worth asking.