How does a helicopter pilot execute an auto-rotation landing?
I am going to assume that by &quot;critical&quot;, you mean survivable.  I will also assume that the engine failure occurs at a height which will kill you.
It's not so much critical steps, it's critical outcomes.  The single most critical outcome is to preserve, or regain, rotor RPM.  What steps are needed to do this will depend on what the aircraft is doing when the engine quits and, to a lesser extent, the type of the helicopter.  I will generalise for an &quot;average&quot; helicopter in straight and level flight.
The immediate action that is drilled into everyone from the very earliest hours as a student is to lower the collective.  Doing this has three effects.  It removes the positive pitch from the blades which removes most of the drag, it aligns the rotor thrust vector with the axis of rotor rotation therefore not using rotor energy for anything except lift and it causes a clutch to disengage the rotor from the engine allowing it to freewheel.  From this point onwards, you are heading back towards earth.
The second immediate action at the same time as lowering the collective (assuming forward flight) is to pull back on the cyclic to flare.  This loads the disc which causes it to &quot;cone&quot; upwards which reduces the disc diameter.  Therefore, the centre of gravity of the disc moves inwards and due to conservation of angular momentum, the rotor RPM increases.  For quite complex reasons, the nose of the helicopter will also pitch down when the collective is lowered so pulling back counters that tendency.
The third immediate action is to push in the pedal on the opposite side to the rotation of the blades. If the blades rotate counter clockwise (to the left as the pilot sees it) you push in right pedal to reduce the thrust which is produced by the tail rotor which is no longer countering the yaw caused by the drag from the powered rotor.  This is less critical than the first two and although it can be dangerous and get you into an uncomfortable attitude, it is usually possible to recover from not pushing the pedal in immediately.  If you've got rotor RPM, then you can sort it out.
Now you have successfully entered autorotation.  From here, fly more or less normally to the next critical point which is about 50' off the ground.
What you've done is to ensure that the rotor has flying RPM and that you are managing energy by trading potential energy (height) for kinetic energy (rotor RPM).  The conversion is done by the airflow which now comes from under the disc and &quot;drives&quot; the rotor to maintain RPM.  The pitch is neutral, or maybe even negative but, the relative airflow is now upwards through the disc and therefore, the blades have a positive angle of attack and generate some lift.  This stops the helicopter from falling.  There is some drag generated as a consequence of generating that lift, but it is easily overcome by the power which is now driving the rotor from that upward airflow.
As long as you are descending, that conversion will happen and your RPM will be maintained.  The controls are rigged such that with the collective fully down, RPM will remain in the normal range.  Sometimes you have to tweak it a little with small amounts of collective, flares and turns but in general, you just fly towards your landing spot.  The allowed RPM range is greater in autorotation.  For example (and from memory), the R22 has a range of 97-103% in normal flight and 90-110% in autorotation.
You are now descending with a high rate of descent and usually, significant forward speed.  You need to reduce both of those to get to a safe arrival. To do this, there are three more critical steps.
Starting at about 50 feet (depending on lots of factors but let's stick with the average helicopter which entered autorotation from straight and level with significant altitude), you flare the aircraft by pulling back on the cyclic.  This will immediately begin to slow the aircraft.  It will also begin to increase RPM (you are now converting speed into rotor kinetic energy).
At the same time, you increase collective to reduce the rate of descent by increasing the lift generated.  This will rapidly increase the drag, but now the energy needed to maintain the RPM is coming from the flare which is converting speed into RPM.  You also need to put in pedal to stop the aircraft from yawing as the drag increases on the rotor.
Providing you get the entry right and your flare reduces the speed and rate of descent to something survivable, then you will walk away.  You might wreck the helicopter and break some bones, but arrive at 10 feet with only 20 knots and 150 feet per minute rate and you'll get away with it.
If you are well trained and in practice, then you will land safely and smoothly with no damage to  machine or people.
In summary, critical steps:

Entry.  Lever down, cyclic back, pedal in.
Arrival.  Cyclic back, lever up, pedal in.