How does one Realize emptiness? Are there specific practices, meditation instructions, intended to identify and realize/experience emptiness? Is this different than realizing non-self, or the emptiness of the self? or the emptiness of other/objects?
So now we go for the Zen view.  Or I should say Rinzai view.  I want to first pat you on the back. You are absolutely right to say "realize" emptiness.  Please do not try to understand it.  That's a complete waste of time.  I'm not sure if you intended the question this way, but what you are asking for, specifically in your inquiry regarding the emptiness of other things/objects, is nothing less than a request for a full exploration of the path.  I will try to be brief as I can.  The short answer is that you need to sit and that you need to find a teacher.  The long answer follows.  

When you first walk into the zendo, your teacher will normally tell you to watch your breath much in the way taught in anapanasati.  Here, you begin to develop and collect your mind.  As your sitting deepens and your focus improves - and this may happen over the course of months or even years - you will begin to notice one of any number of phenomenon.  For some people, it feels like your body is expanding, for others your body may disappear, and for still others, your head may feel like it's twisting.  What you experience isn't necessarily as important as that the experiencing is happening.  This is your first glimpse of samadhi.  In the ten oxherding pictures, this is seeing the ox's tracks for the first time.
      

Upon seeing the tracks, the next thing that your teacher will do is give you the Mu koan.  This practice uses the collected mind you developed with anapanasati and directs it toward an actual experience of emptiness.  On every out breath, you will say "muuuuuuuu".  As the Pali suttas say, you will follow this for the whole body of the breath with the most important place being the very end of your exhalation right before you inhale.  As this practice deepens, you will begin to notice a blankness.  This is your first glimpse of emptiness and it usually happens completely by accident.  In the ox herding series, this is seeing the ox's butt sticking out from behind a bush.  Your next task is to make that experience habitual.  This is grabbing the ox's reins.  To hold the reins is to generally know where the ox is at all times and how to find him when you need him.  With the ox's reins firmly in hand, your next task is to gain mastery over the experience.  In essence, you are deepening your command of body, breath, and mind.  This is taming and leading the ox.  With the ox tame, you may now ride him.  This is becoming one with emptiness or one with Mu.  As Master Mumon says, here "all the illusory ideas and delusive thoughts accumulated up to the present will be exterminated, and when the time comes, internal and external will be spontaneously united. You will know this, but for yourself only, like a dumb man who has had a dream."  At this point, you will be asked to call Mu by your teacher.  Your calling of mu will demonstrate how well internal and external are united...how well you, the ox, mu, the body, emptiness, the breath, and mind have all become one thing.  Getting to this point can take years.

And with that, your Zen training wheels come off.  From here on out, emptiness is no longer a realization.  Instead, it becomes a tool that you will use for the remainder of your training.  After you answer the Mu koan, you will begin to work through any number of other koans.  Zen calls this climbing the mountain of swords that is riddled with the skulls of the fallen.  And it can be every bit as daunting as that description implies.  Each koan forces you to confront some aspect of yourself - some fear, attachment, belief, etc. - that is keeping you from true enlightenment.  But rather than working with these things intellectually as you might in therapy, you approach these karmic impediments from the experience of emptiness.  The deeper you go into mu [emptiness], the better the insight you gain, and the more likely you are to unshackle yourself from these obstacles.  The entirety of this practice is a dance between the world of form and the world of emptiness.  You delve into emptiness in your sitting and you bring it back to the world of form in your probing of the koan you are working with.  

Bit by bit, koan by koan, year after year, sesshin after sesshin, the wall between you and enlightenment breaks down.  Eventually, it will fall away completely.  At the moment of enlightenment, the very separation between the world of form and emptiness dissolves entirely.  You will know, just as intimately as the feeling of your butt against the cushion, what the Heart Sutra means when it says that "form is emptiness and emptiness is form".  You will directly see the emptiness of all things - of yourself, objects, thought...the entire universe.

And then you get to be the fat old Buddha who gets drunk with the butchers and generally causes a nuisance in the town below.  Happy sitting!