To get this core idea, there are hundreds of gates. Just describing three of them:
a.) Way of the heart - compassion
Finding out what one can do to help this world struggling with violence will help. The most complete and absolute form of help (throwing shoes at so called 'environmental criminals' is NOT one :D) one can do in every moment of ones existence will lead us.
b.) Way of the intellect - ego
Identify every place the ego is hiding. Places where we seek our ego - words of others in the form of honor and pride, career and ambition, happiness in the form of events, material progress etc. Having a sharp intellect and finding out every place where the ego is hiding and cutting through it with the sharp intellect will help.
c.) Way of stillness
First understand that for most people the mind is diseased as it cannot stay still even in the presence of glorious natural beauty, let alone the mundane. Seeking to try and get the mind to stay in the moment and seeking to understand its incessant chattering will help.
The three ideas are interconnected of course. But to begin with, I think its fine to not consider that. Any one of these gates (also the countless gates not listed here) when held on to sincerely, will lead us to the understanding of the core idea.