What is "meditation on the deathless state (nirvana)"?

Said to the Blessed One: “Venerable sir, it is said, ‘the Deathless, the Deathless.’ What now, venerable sir, is the Deathless? What is the path leading to the Deathless?”

“The destruction of lust, the destruction of hatred, the destruction of delusion: this is called the Deathless. This Noble Eightfold Path is the path leading to the Deathless; that is, right view … right concentration.”

“Venerable sir, it is said, ‘the removal of lust, the removal of hatred, the removal of delusion.’ Of what now, venerable sir, is this the designation?”

“This, bhikkhu, is a designation for the element of Nibbāna: the removal of lust, the removal of hatred, the removal of delusion. The destruction of the taints is spoken of in that way.” sn45.7

"And what is the development of concentration that, when developed & pursued, leads to the ending of the effluents? There is the case where a monk remains focused on arising & falling away with reference to the five clinging-aggregates: 'Such is form, such its origination, such its passing away. Such is feeling, such its origination, such its passing away. Such is perception, such its origination, such its passing away. Such are fabrications, such their origination, such their passing away. Such is consciousness, such its origination, such its disappearance.' This is the development of concentration that, when developed & pursued, leads to the ending of the effluents. An4.41

"Monks, the ending of the effluents is for one who knows & sees, I tell you, not for one who does not know & does not see. For one who knows what & sees what is there the ending of effluents? 'Such is form, such its origination, such its disappearance. Such is feeling, such its origination, such its disappearance. Such is perception, such its origination, such its disappearance. Such are fabrications, such their origination, such their disappearance. Such is consciousness, such its origination, such its disappearance.' The ending of the effluents is for one who knows in this way & sees in this way.

"The knowledge of ending in the presence of ending has its prerequisite, I tell you. It is not without a prerequisite. And what is the prerequisite for the knowledge of ending? Release, it should be said. Release has its prerequisite, I tell you. It is not without a prerequisite. And what is its prerequisite? Dispassion... Disenchantment... Knowledge & vision of things as they actually are present... sn12.23

He regards whatever phenomena there that are connected with form, feeling, perception, fabrications, & consciousness, as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a disintegration, an emptiness, not-self. He turns his mind away from those phenomena, and having done so, inclines his mind to the property of deathlessness: ‘This is peace, this is exquisite—the pacification of all fabrications; the relinquishment of all acquisitions; the ending of craving; dispassion; cessation; unbinding.’

“Staying right there, he reaches the ending of the effluents. Or, if not, then—through this very Dhamma-passion, this Dhamma-delight, and from the total ending of the five lower fetters—he is due to arise spontaneously (in the Pure Abodes), there to be totally unbound, never again to return from that world.mn64

"A virtuous monk, Kotthita my friend, should attend in an appropriate way to the five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. Which five? Form as a clinging-aggregate, feeling... perception... fabrications... consciousness as a clinging-aggregate. A virtuous monk should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. For it is possible that a virtuous monk, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of stream-entry."

"Then which things should a monk who has attained stream-entry attend to in an appropriate way?"

"A monk who has attained stream-entry should attend in an appropriate way to these five clinging-aggregates as inconstant, [...] not-self. For it is possible that a monk who has attained stream-entry, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of once-returning."

"Then which things should a monk who has attained once-returning attend to in an appropriate way?"

"A monk who has attained once-returning should attend in an appropriate way to these five clinging-aggregates as inconstant, [...] not-self. For it is possible that a monk who has attained once-returning, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of non-returning."

"Then which things should a monk who has attained non-returning attend to in an appropriate way?"

"A monk who has attained non-returning should attend in an appropriate way to these five clinging-aggregates as inconstant, [...] not-self. For it is possible that a monk who has attained non-returning, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of arahantship."

"Then which things should an arahant attend to in an appropriate way?"

"An arahant should attend in an appropriate way to these five clinging-aggregates as inconstant, [...] not-self. Although, for an arahant, there is nothing further to do, and nothing to add to what has been done, still these things — when developed & pursued — lead both to a pleasant abiding in the here-&-now and to mindfulness & alertness." Mn22

"The subduing of desire-passion for feeling, the abandoning of desire-passion for feeling: That is the escape from feeling. Sn36.23

we enter upon and abide in the cessation of perception and feeling. And our taints are destroyed by our seeing with wisdom mn31

“On one occasion, friend Ānanda, I was dwelling right here in Sāvatthī in the Blind Men’s Grove. There I attained such a state of concentration that I was not percipient of earth in relation to earth; of water in relation to water; of fire in relation to fire; of air in relation to air; of the base of the infinity of space in relation to the base of the infinity of space; of the base of the infinity of consciousness in relation to the base of the infinity of consciousness; of the base of nothingness in relation to the base of nothingness; of the base of neither-perception-nor-non-perception in relation to the base of neither-perception-nor-non-perception; of this world in relation to this world; of the other world in relation to the other world, but I was still percipient.”

“But of what was the Venerable Sāriputta percipient on that occasion?”

“One perception arose and another perception ceased in me: ‘The cessation of existence is nibbāna; the cessation of existence is nibbāna.’ Just as, when a fire of twigs is burning, one flame arises and another flame ceases, so one perception arose and another perception ceased in me: ‘The cessation of existence is nibbāna; the cessation of existence is nibbāna.’ On that occasion, friend, I was percipient: ‘The cessation of existence is nibbāna.’” an10.7

Site doesn't allow more than 8 links without rep but i'll add here some excerpts illuminating the training;

A verse;

If one were to have mindfulness always established, continually immersed in the body, (thinking,) "It should not be, it should not be mine; it will not be, it will not be mine"[1] — there, in that step-by-step dwelling, one in no long time would cross over attachment.ud7.8

This passage can also be translated as:

It should not be, it should not occur to me; it will not be, it will not occur to me.

"There is the case, Ananda, where a monk, having practiced in this way — (thinking) 'It should not be, it should not occur to me; it will not be, it will not occur to me. What is, what has come to be, that I abandon' — obtains equanimity. He relishes that equanimity, welcomes it, remains fastened to it. As he relishes that equanimity, welcomes it, remains fastened to it, his consciousness is dependent on it, is sustained by it (clings to it). With clinging/sustenance, Ananda, a monk is not totally unbound."

"Being sustained, where is that monk sustained?"

"The dimension of neither perception nor non-perception."

"Then, indeed, being sustained, he is sustained by the supreme sustenance."

"Being sustained, Ananda, he is sustained by the supreme sustenance; for this — the dimension of neither perception nor non-perception — is the supreme sustenance. There is [however] the case where a monk, having practiced in this way — 'It should not be, it should not occur to me; it will not be, it will not occur to me. What is, what has come to be, that I abandon' — obtains equanimity. He does not relish that equanimity, does not welcome it, does not remain fastened to it. As he does not relish that equanimity, does not welcome it, does not remain fastened to it, his consciousness is not dependent on it, is not sustained by it (does not cling to it). Without clinging/sustenance, Ananda, a monk is totally unbound." Mn106

"Any consciousness whatsoever that is past, future, or present; internal or external; blatant or subtle; common or sublime; far or near: every consciousness is to be seen as it actually is with right discernment as: 'This is not mine. This is not my self. This is not what I am.'

"Seeing thus, the well-instructed disciple of the noble ones grows disenchanted with form, disenchanted with feeling, disenchanted with perception, disenchanted with fabrications, disenchanted with consciousness. Disenchanted, he becomes dispassionate. Through dispassion, he is fully released. With full release, there is the knowledge, 'Fully released.' He discerns that 'Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world Sn22.59