How do helicopter pilots practice auto rotation?
It seems that you already understand what an autorotation is but for the benefit of other readers, I'll recap what the flare  is all about.

There are two really critical parts of an autorotation.  The entry and the flare.  If you get the entry wrong, then there is no autorotation.  You become a passenger all the way to  the scene of the crash.

If you get the flare very wrong (not enough speed when you flare or flaring far too high), you become a passenger all the  way to the scene of the crash.

If you make a mess of the flare, perhaps plenty of speed but too early, or too late, or not enough speed but flaring at a good height, then you will survive.  You might not get to use the helicopter again and you might spend some time in hospital but you're not going to  hit the  ground with enough energy to ruin all your mushy internal parts.

The reality is that most GA and low hour pilots faced with a real autorotation have a high chance of messing up the flare, and the subsequent touch down, damaging themselves and the machine but surviving.  The accident statistics and reports confirm this.  Chopping off the tail and rolling over are common outcomes of real autos.

In training and practice, the idea is that you walk away and get to use the helicopter again.

So, what height is the "right" height for the flare?

The POH emergency procedures section will also detail the height but, it will use slightly vague words such as "about 50 feet".  This is because most practice autorotations end with you at 50 feet with around 60kts airspeed and the nose straight - "the ideal autorotation".  The are many factors which affect this, mainly weight and wind (ideal ones always finish into wind).

Take a look at the "height velocity" diagram for a typical GA/sport helicopter.



(Source Rotorwandwing.com)

The shaded areas show the combinations of height and velocity from which a successful safe landing cannot be accomplished in autorotation.  When you flare, you are going to be close to the ground.  You have no choice in that!  When you start the flare, you want to be well away from the shaded areas of the diagram.  A normal autorotation aims for an entry into the flare with 55-65 kts airspeed.  Look at the diagram again and note that being at around 40-50 feet at that speed is well away from the shaded areas - bang in the middle of the "safe corridor".  This is the area you are aiming for.  At this point, you have enough energy, both kinetic and potential, to land safely. 

You can see why flaring too high, too low or with not enough speed can lead to a bad weekend if you make a mess of it or, a permanent removal of flying privileges if you get it really wrong.

Hopefully this gives you a good idea of what the "right height" means.

When doing ab-initio training, you are gently led into autorotations. Your instructor will demonstrate one to you very early.  If you are clearly confident and not nervous, maybe on the first lesson which my instructor did.  Indeed, at my school, every single dual flight included at least one demonstrated or practice autorotation so you get a feel for the height early on.

You will also, perhaps every time (I think this is true in the US) finish an autorotation with a power recovery.

I chose that video because there's a good illustration in it of how to judge the height - and given that "about" is as good as the POH gives you, it's all about judgement.  In this video, you can see everything.  Watch it and look straight ahead.  Do not look at the ground, let your peripheral vision do the work. Notice how as you get closer to the ground, it seems to be coming towards you at a constant rate then suddenly, it seems to rush towards you - the "ground rush"?  That's when you start the flare.  You already know from the power recoveries you've practiced and the demonstrations what the correct height looks like so you know roughly when to flare but that sudden ground rush is the sure sign that now is the time to start slowing down.

What you are aiming for is to arrive at 0 rate of descent at or just above the ground so that a little bit of collective can be used to cushion the touch down.  With some wind on the nose and good airspeed, it is possible to bleed off most of the descent rate and ground speed with the flare.  A skilled pilot might not even use collective until the last couple of feet for a really gentle 0-0 touchdown.

There are a lot of different kinds of autorotations and some advanced ones don't use flare at all - or very little flare from low speed.  Really skilled pilots in light helicopters can go more or less vertically down with just enough airspeed to keep translational lift.

In summary, good judgement which is arrived at from the POH reinforced with demonstrations and practice.

Note to other rotary pilots:  I know that using the HV diagram is not how it's trained but it's useful in my opinion to understand what the correct height is.