Smooth airflow (brighter is faster)
Separated, turbulent airflow

Air flows from left to right. Raise the angle of attack and watch the top of the wing.

Stall simulator

A wing section in a wind tunnel, seen from the side. Raise the angle of attack and watch the smooth airflow over the top break down as the wing reaches its critical angle of attack.

Angle of attack

Between the chord line and the relative wind 4.0°

Stall warning

Airflow: Smooth over the whole wing
Lift: Increasing with angle of attack

Lift coefficient

Lift rises steadily with angle of attack until the critical angle of attack. Past it, the airflow separates, lift falls off, and drag climbs fast. This simulated wing stalls at 16°.

What to take away

A wing stalls when it exceeds its critical angle of attack. That angle doesn't change with weight, airspeed, or attitude, so you can stall at any airspeed, in any attitude, at any power setting.
The stall speeds in the POH are just the airspeeds where a wing reaches that angle in particular conditions. Heavier weight, a steeper bank, or more G load raises the stall speed.
Separation starts at the trailing edge and creeps forward. You often feel it first as buffet, and the stall warning comes on a few knots before the stall.
To recover, reduce the angle of attack first: lower the nose (or release back pressure) until the stall warning stops. Then level the wings, add power as needed, and return to your flight path.
Trainer wings are designed so the root stalls before the tips, which keeps the ailerons working as the stall develops.

The airflow is computed for an idealized airfoil, with separation added to match how a real wing stalls. The angles are typical of a light-airplane wing, not a specific airplane. Real critical angles of attack are usually somewhere around 15° to 20°.

Sources

FAA-H-8083-25C, Pilot's Handbook of Aeronautical Knowledge, Chapter 5, Aerodynamics of Flight
FAA-H-8083-3C, Airplane Flying Handbook (slow flight, stalls, and stall recovery)
AC 120-109A, Stall Prevention and Recovery Training