At any angle of attack beyond C_lmax, the airflow can no longer follow the upper surface of the wing and the flow separates and the wing loses lift.  The weight exceeds the lift so the plane accelerates downward.

Power-on: Associated with takeoff and climb
Power-off: Associated with landings in the approach configuration
Accelerated Stalls: Caused by an abrupt or excessive control movements.  They commonly occur during maneuvers involving a high load factor or a sudden change in the flight path.  For example, a steep turn or a rapid dive.  Any time you are experiencing an increased flight load factor, that acceleration indicates that you have increased the angle of attack, and even though you may be well above the usual stall speed, you will be closer to the stalling angle of attack.
Secondary Stall: If you pull up too quickly during recovery from a stall, the angle of attack is increased too quickly or you didn't decrease it enough in the first place.
Cross-control Stall:  This occurs when the flight controls are crossed, meaning that rudder pressure is being applied in one direction while ailerons are applied in the opposite direction.  The most likely time for this is during a poorly executed turn to final approach for a landing.  Often these stalls occur with little warning and insufficient altitude for recovery.
Elevator Trim Stall:  Most likely occurs during a go-around from a landing approach.  The airplane is trimmed for a slow speed with a lot of nose up trim.  When the power is applied for the go-around, the normal tendency is for the nose to pitch up and if positive pressure is not used to counteract the strong trim forces, the nose will continue to pitch up.  In addition, since full power is applied, the aircraft is subject to the left turning forces easily putting it in uncoordinated flight.

Most airplanes warn the pilot in a variety of ways.  Most general aviation aircraft have a stall horn or light which is just an angle of attack indicator.  As airflow begins to separate from the wing, there is often a buffeting or shaking through the entire airframe.  At low airspeeds, the controls often feel mushy and you may notice the sound of air rushing along the fuselage fading away.

The first priority in recovery from a stall is to reduce the angle of attack with forward elevator to allow the wings to regain lift.  This may consist of merely releasing back pressure, or you may have to firmly move the elevator control forward.  Excessive forward movement of the yoke however, may impose a negative load on the wings and delay the stall recovery.  The next step, which should be accomplished almost simultaneously, is to smoothly apply maximum power to increase airspeed and to minimize the loss of altitude.  As airspeed increases, adjust power to return the airplane to the desired flight recovery, coordinated use of the controls is especially important.