Where to add a capacitor

The transistor may act as a switch or a variable resistor. If no voltage is applied to the base (more precisely: no current flowing into the base) then the switch is open. As base current is applied it gets amplified by the transistor into an N times larger collector current. The "N" is an important transistor parameter, called \$H_{FE}\$, and it defines the current amplification factor. For general purpose transistors this is often around 100.

So if you apply a base voltage (you need a series resistor!) so that there will flow, say, 1 mA, then there will be 100 mA collector current if the circuit allows it. That means that other components may limit that current to a lower value. Let's assume your LED has a 2 V voltage drop, that will be rather constant for that type of LED. Then assuming the transistor is fully conducting (no voltage drop between collector and emitter) you'll have 9 V battery voltage - 2 V LED voltage = 7 V across the resistor. If we choose a resistor value of 350 Ω then, according to Ohm's Law we have a current of 7 V/ 350 Ω = 20 mA through that resistor and therefore also through the LED. (20 mA is a typical current for an indicator type of LED.)
So, while the transistor would like to draw 100 mA, the resistor will always limit that to the lower 20 mA.

You don't say what the signal from the amplifier is. Is that a line level (500 mV) or a speaker output level (3 V for 1 W)? In the first case the voltage will be too low; a transistor's base has to be at 0.7 V minimum before current starts to flow. If you use the speaker output you can use a 1 kΩ resistor in series with the output to limit the base current.

Also place a diode (1N4148) in anti-parallel with the base: cathode to the base, anode to ground. This prevents too large negative voltages across the base, which would destroy the transistor.

How could it be destroyed? Voltage is merely 0.15 volts (according to multimeter)

If it were 0.15 volts and the speaker was an 8 ohm speaker, the power output to the speaker would be 0.15*0.15/8 = 0.028 watts. Does this seem likely or does it seem more likely that the multimeter isn't giving you the full picture?

If in fact you were driving 1 watt into the speaker, the RMS voltage would be 2.828 volts with a peak voltage of that is significantly higher maybe 4 to 10 volts for music type signals.

This level of voltage and the level of current that the amplifier output is capable of providing will certainly damage an ADC input on a chip. Next time use a 10k resistor in series and maybe also a coupling capacitor.