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The sages were worried about the Kali Yuga and they assembled at the beginning of Kali Yuga in Naimisranya to ask Suta Goswami this same question. In response to this, the text Srimad Bhagavatam was spoken by Suta Goswami to all present.

So as a Hindu, one would regularly read and apply Srimad Bhagavatam to counter the effects of Kali Yuga. 

In the Srimad Bhagavatam, the most essential instruction given is to the chant the names of Krishna. Infact that is the blessing of this age. Despite all the bad effects of Kali yuga, it has the greatest blessing that simply by chanting Krishna, one can be delivered from this material world.

Srimad Bhagavatam has answers to all your doubts.

SB 12.3.45: In the Kali-yuga, objects, places and even individual personalities are all polluted. The almighty Personality of Godhead, however, can remove all such contamination from the life of one who fixes the Lord within his mind.

SB 12.3.46: If a person hears about, glorifies, meditates upon, worships or simply offers great respect to the Supreme Lord, who is situated within the heart, the Lord will remove from his mind the contamination accumulated during many thousands of lifetimes.

SB 12.3.47: Just as fire applied to gold removes any discoloration caused by traces of other metals, Lord Viṣṇu within the heart purifies the minds of the yogīs.

SB 12.3.48: By one's engaging in the processes of demigod worship, austerities, breath control, compassion, bathing in holy places, strict vows, charity and chanting of various mantras, one's mind cannot attain the same absolute purification as that achieved when the unlimited Personality of Godhead appears within one's heart.

SB 12.3.49: Therefore, O King, endeavor with all your might to fix the Supreme Lord Keśava within your heart. Maintain this concentration upon the Lord, and at the time of death you will certainly attain the supreme destination.

SB 12.3.50: My dear King, the Personality of Godhead is the ultimate controller. He is the Supreme Soul and the supreme shelter of all beings. When meditated upon by those about to die, He reveals to them their own eternal spiritual identity.

SB 12.3.51: My dear King, although Kali-yuga is an ocean of faults, there is still one good quality about this age: Simply by doing Hari Kirtan, one can become free from material bondage and be promoted to the transcendental kingdom.

SB 12.3.52: Whatever result was obtained in Satya-yuga by meditating on Viṣṇu, in Tretā-yuga by performing sacrifices, and in Dvāpara-yuga by serving the Lord's lotus feet can be obtained in Kali-yuga simply by doing Hari Kirtan.

This is the most important, but perhaps also least understood statement:

"SB 12.3.48: By one's engaging in the processes of demigod worship, austerities, breath control, compassion, bathing in holy places, strict vows, charity and chanting of various mantras, one's mind cannot attain the same absolute purification as that achieved when the unlimited Personality of Godhead appears within one's heart."

In Kaliyuga, no divine interventions are to happen, except at the very last phase. Which means, however much we get inspired, hopeful and keen based on the puranic lores we read, nothing's gonna happen.

What does this mean for us then? Where does this leave us?

It leaves us in our own hands.

And that's exactly had been the message of Gautama Buddha and all the Yogis till date (under Kriya and Raja Yoga paramparas).

No avatar is going to deliver salvation in this age - you need to do it for yourself. EVERY ONE of us - independently - need to do it for oneself. You cannot do it for the next person.

Look inwards - the cosmos and the Supreme Godhead are all found inside.