What is our true self and how we can connect with it?

The true self is the soul. The soul is an atomic particle of consciousness, which at the present moment is covered by the physical and psychic layers in the form of the body and the mind. By purifying the mind one can connect with the real self.

"The soul is atomic in size and can be perceived by perfect intelligence. This atomic soul is floating in the five kinds of air [prana, apana, vyana, samana and udana]. The soul is situated within the heart, and it spreads its influence all over the body of the embodied living entities. When the soul is purified from the contamination of the five kinds of material air, its spiritual influence is exhibited." -- Mundaka Upanishad, 3.1.9

So we have to clean the mind in order to to perceive the soul. Just like physical objects are cleansed with water, psychic or mental objects are cleansed with sound. The highest cleansing power is the sound of God's name.

That which covers us and keeps us from realizing our real selves, is our mind. The mind consists of thoughts, feelings, willpower, discrimination (intelligence) and false ego. Those are like screens that cover the pure consciousness of the self.

We are all eternal souls - minute particles of Krishna's consciousness. Krishna's consciousness consists of eternity, knowledge, and bliss, so we are minute particles of eternity, knowledge and bliss, But these minute particles of pure consciousness are at the moment covered by physical and mental layers in the form of the body and mind.

All souls, regardless of what kind of body they inhabit - plants, insects, fish, reptiles, birds, animals, or humans - are minute particles of eternity, knowledge, and bliss. That's why all living entities always gravitate towards these three conditions - eternity, knowledge, and bliss. All living entities are pleasure seeking, they try to develop knowledge, and they don't want to die, they possess the survival instinct.

The sound of Krishna's name will purify the filter of the mind, so that we can connect to our real selves. By chanting Krishna's name we will experience higher forms of knowledge and bliss. That is a testable prediction that can be investigated scientifically.

This is not some belief. It’s a scientific process as asserted by Krishna in the Bhagavad Gita, which will work whatever is our belief.

It doesn't matter whether you are an Atheist, Buddhist, Hindu, Christian, Mohammedan, Republican or whatever, if you chant the Hare Krishna mantra on a regular basis, you will connect to your real self beyond your thoughts, feelings and false ego, and when you contact your real self, it will be experienced as knowledge and bliss.

The wonderful thing about this religion, the Vaishnava religion, is that you do not have to become a Hare Krishna and shave your head, dress in sheets, and go out on the streets dancing and singing. You can sit right in your own living room and test it.

Just try to chant the following mantra -

hare krishna hare krishna krishna krishna hare hare

hare rama hare rama rama rama hare hare

... say, 10 minutes a day for a week and see where it takes you.

That's BRAINWASHING, I hear someone yell :)

That's right. Our mind is unclean. Our mind has been polluted by impure impressions accumulated throughout so many lives. It needs to be washed. And you wash the mind by the sound of God's name.

hare krishna hare krishna krishna krishna hare hare

hare rama hare rama rama rama hare hare

The above mantra consisting of 16 words and 32 syllables, is the only means by which to protect against the evil influence of this age of Kali. By researching all the Vedas, one will find no more sublime process of religion than to recite the Hare Krishna mantra.

(Kali-santarana Upanishad)