As said above, a vast topic
I think one of the problems we have with it is that in the West, emptiness is associated with anomie, or with alienation and meaninglessness. 'I feel so empty' is associated with feelings of disillusionment and abandonment, perhaps after the loss of a relationship or a loved one. But it means something quite different in Buddhist philosophy. In Buddhism 'realizing emptiness' means realizing that nothing has any absolute, fixed or unchanging reality. The main point of this is to overcome the ego's instinctive dependence on external things as sources of security. We generally identify with such things and invest them with great significance. However we start to see that all of the things that we usually invest with such significance, are also dependent on causes and conditions, in other words, they come together and fall apart in time, as does everything and everyone else. That is the key message of emptiness, but it needs to be tempered with compassion. Through compassion the sense of the 'otherness' of those around us is dissolved. This leads to a sense of being together with others, rather than withdrawal into some kind of emotional vacuity. That is the active side of emptiness, namely, bodhicitta
. The teachings say that when bodhicitta arises, then the insubstantiality of things is not threatening or alienating, but appears as a sense of non-attachment or naturalness (as per this talk
by Lama Yeshe).
So that is a very good question to ask. 'Realizing emptiness' is something that can be accomplished spontaneously and intuitively, through meditation and the other means, such as studying the teachings and indeed there are many very profound sutras and teachings about this question, so it is a matter of meditating on them and reflecting constantly on their meaning. It is not necessarily an easy thing to grasp, but well worth the effort.
Learn to do good, refrain from evil, purify the mind ~ this is the teaching of the Buddhas