Radio Principles

As you can see the signal from the detector is capacitively coupled to the inverting input at pin 2. This reduces overloading. There is a potentiometer to act as a volume control. The non-inverting input at pin 3 is referenced to ground. Pin 4 is the ground connection, and output is achieved at pin 5 via an LR filter to reduce noise and a large capacitor in series with the speaker helps a fidelity of tone. Pin 6 is the supply voltage and has a capacitor to ground to remove stray AC interference, pin 7 is optional and is there to reduce a whistle created within the amplifier itself under certain signal conditions. Between pins 1 and 8 is a 10 microfarad capacitor; this allows a gain of 200. Without it the amplifier will have a gain of 20, and by combining resistors and capacitors we can vary the gain. We can in fact dispense with all components except those on pin 5, and even then the ferrite bead and 47 ohm resistor are not necessary, but we risk a higher signal to noise ratio at the speaker.
Most commercial receivers will now use an LM386 or something similar (meatier ones up to 30W are available) as the cost of the chip is actually lesser than that of a transformer.