A receiver has three jobs: pick the one signal you want out of thousands, boost it until it is big enough to use, and turn it back into sound (or data). Every receiver design, from a crystal set to a software-defined radio, is a different way of doing those three things.
Antenna to speaker
Each stage does one job. The wanted signal (teal) starts tiny among stronger neighbours (grey) and ends as sound. Sketches are illustrative.
Antenna. It delivers every signal on its frequency range at once, microvolts or less, in a sea of noise.
RF stage. A band-pass filter rejects signals far from the band you are tuned to; an optional amplifier adds a little gain ahead of the noisiest later stages.
IF filter. The narrow filter that does most of the selecting. Its width sets how much of the band you hear; see Filters in radios.
Detector. Recovers the message from the radio signal. The kind depends on the mode.
Audio amplifier. Raises the audio to speaker or headphone level.
An AGC circuit watches the signal level at the end of the IF chain and turns the gain down for strong signals, so loudness stays steady (see AGC, noise blankers and noise reduction).
The detector depends on the mode
Mode
Detector
What it does
AM
envelope detector
follows the rising and falling amplitude of the carrier
SSB, CW, digital audio
product detector
mixes the signal with a locally made carrier (the BFO), leaving the audio as the difference
FM
discriminator or quadrature detector
turns frequency changes into voltage changes
SSB has no carrier of its own to follow, so the receiver supplies one. If that carrier is a little off, voices sound too high or too low; this is why SSB needs accurate tuning (see RIT, XIT and split operation).
Why all the stages?
Gain alone does not make a receiver: amplifying everything amplifies the strong neighbours too, and the noise. The art is amplifying after enough filtering, and filtering where it is easiest. A tuned filter narrow enough to pass one SSB signal is hard to build at 14 MHz, and harder still to retune across a band, which is the reason most receivers shift the signal to a fixed frequency first.
Sensitivity: how weak can it hear? Selectivity: how close can it tell apart?
The quality of that job is described by sensitivity (hearing weak signals), selectivity (separating close ones) and dynamic range (coping with strong ones): see Sensitivity, selectivity and dynamic range.