Śrīla Bhakti Sundar Govinda Dev-Goswāmī Mahārāj explains the process given by Śrīman Mahāprahu to chant the Holy Name.
We say yajña means fire sacrifice, but that is not the actual meaning. Something done for the satisfaction of Lord according to a regulated (vaidīka) method is a yajña. The śrutis, the Vedas, say that yajña is one kind of manifestation of Viṣṇu. Yajño vai Viṣṇuḥ iti śruteḥ. This is the evidential verse in the Vedas. Śrīmad Bhāgavat also says yajñaiḥ saṅkīrtana-prāyair yajanti: we should perform worship through the yajña of saṅkīrtan. If only there is a fire, then that is not a ful expression of yajña. The real fire of yajña is not a fire that burns visibly; it is a fire that burns our karma, and through that heavenly feelings arise within us.
You know the first verse of the Śikṣāṣṭakam. There, Mahāprabhu has given a very nice expression of His saṅkīrtan-yajña.
ānandāmbudhi-vardhanaṁ prati-padaṁ pūrṇāmṛtāsvādanaṁ
sarvātma-snapanaṁ paraṁ vijayate śrī-kṛṣṇa‑saṅkīrtanam
Chaitanya Mahāprabhu composed eight verses. He did not actually give much attention to composition; His verses, these eight verses, came out automatically from His lotus mouth. This is the first of them. He did not write any books but gave only these eight verses, maybe two or three others, but not more. His divine will was fulfilled by the six goswāmīs; they composed so much.
Hari-saṅkīrtan first cleans our mind. The mind is a like mirror covered by so much dust. With it, we cannot see our own self. But when this mirror is cleaned by Hari-saṅkīrtan, then we can see our own self. This is the first result that comes through Hari-saṅkīrtan: cheto-darpaṇa-mārjanam.
In this material world, the jīva-souls are suffering from so many disturbances because of their karma. It is as though they are burning in a fire in the jungle. Sadness, unhappiness, attachment, detachment—many things come into the minds of the jīva-souls, and because of that they feel so much pain. Dāvāgni means a fire in the jungle that arises automatically. Through saṅkīrtan, that kind of pain goes away forever: bhava-mahādāvāgni-nirvāpaṇam. That kind of fiery pain and disturbance within the jīva-soul’s mind and subtle body—all of it is removed.
Then, automatically, auspicious moonlight (chandrālok) arises for the protection of the jīva-soul and brings joy to the heart of the jīva-soul. Such mercy comes, and everything becomes very peaceful and joyful. Śreyaḥ-kairava-chandrikā-vitaraṇam: śreyaḥ means maṅgal [auspiciousness].
Moonlight automatically gives protection and joy to all living entities. The jīva-souls are burning because of their karma, but with the moonlight of Hari-saṅkīrtan that goes away, peace comes into their minds, they get protection in their spiritual life. Then, pure love—pure beauty, attachment, and ecstasy—are revealed in the heart of jīva-soul, all for their Lord. Eternally feelings come to the jīva-soul, “The Lord is my master, the Lord is my husband, the Lord is my son, the Lord is my father. He is everything: the Lord is my life and soul. Without Him, I cannot live, and with Him, I will have full ecstasy and joy.” Through saṅkīrtan, such feelings come to the heart of the jīva-soul.
Vidyā-vadhū-jīvanam: deeper meaning is also given inside this expression, that is, the feeling of madhura-rasa: the feeling of being newly married, the feeling of a willing and joyful marriage between husband and wife, comes permanently into the heart.
Then, everything in front of the jīva-soul becomes joyful, ecstatic, beautiful, and lovely. More and more, such feelings increase with Lord, and the jīva-soul becomes full satisfied. Pūrṇāmṛtāsvādanam: when someone drinks nectar, satisfaction must come into their heart, and the jīva-soul feels like that.
Then, Mahāprabhu says, “Paraṁ vijayate Śrī-Kṛṣṇa‑saṅkīrtanam: supremely it will get the victory, and we will live under its divine ecstatic shade, the divine merciful shade of Hari-saṅkīrtan.”
This is expression of Chaitanya Mahāprabhu. He as the Yuga-avatār:
The religion in the Kali-yuga is to chant the Holy Name of Lord. Mahāprabhu Śrī Chaitanyadev appeared, organised this, and brought joy to everyone’s heart.
Śrīla Avadhūt Mahārāj: Mahārāj, Mahāprabhu also said, “I have no satisfaction, and I am not qualified to chant the Name.” Many devotees think about only the quantity of the Name and that some kind of easy practice of the Name is possible. Because the Name is advertised so much, they have taken the Name very cheaply. Can you explain Mahāprabhu’s feeling that we are not able to chant the Name?
Śrīla Govinda Mahārāj: In His second verse, Mahāprabhu glorified Hari-nām, the Divine Name:
nāmnām akāri bahudhā nija-sarva-śaktis tatrārpitā
“All power is present in Your Name, and You have manifested so many Forms and Names: Rāma, Kṛṣṇa, Nṛsiṁha, Vāman, Madhusūdan, and so on. You have manifested many of Your Divine Names in this world by Your grace, and You have put all Your power in these Names. So, They are automatically powerful, but I am very unfortunate: I am chanting these Names, but the result of chanting Them is not coming to me. This is my very awkward condition.”
Then, with His next verse, Mahāprabhu explains how way we will get the proper result in chanting:
tṛṇād api sunīchena taror iva sahiṣṇunā
amāninā mānadena kīrtanīyaḥ sadā hariḥ
If you want to get the proper result, you must be like this. You first have to control your environment, which is always giving you trouble. Feel your situation as much as possible: feel how much you can do for yourself. Then, automatically, humility will come to you. Controlling your environment means to not make anyone your enemy. Then, nothing will go against you, and feelings, real feelings, will come into your heart. This is the basis of the three qualities given by Mahāprabhu to chant the mahāmantra.
Śrīla Bhakti Vinod Ṭhākur translated this third verse of Mahāprabhu into Bengali.* The meaning is that you must be humble, be tolerant, and give honour to others. Then, quality will come to you. With that good quality, you can chant the Holy Name of Lord, and that chanting will be fruitful. So, be humble, be tolerant, and give honour to others. This is first condition. And inside that, there are more disturbances to chanting, that is, the ten kinds of offences. We always give everyone a small book where these ten kind of offences are written. If you avoid the offences and chant the Holy Name, the proper result must come to you.
Spoken in St. Petersburg, Russia.
Translation of the third verse of Śrī Śikṣāṣṭakam by Śrīla Bhakti Vinod Ṭhākur:
śrī-kṛṣṇa-kīrtane yadi mānasa tohāra
parama yatane ta̐hi labha adhikāra 
yadi–If tohāra [āchchhe]–you have mānasa–a mind kīrtane–to chant śrī-kṛṣṇa–the Name of Śrī Kṛṣṇa, [then with] parama–great yatane–care, labha–get adhikāra–the qualification ta̐hi–for that. 
If you aspire to chant the Name of Kṛṣṇa, then, with great care, become qualified to do so.
tṛṇādhika hīna, dīna, akiñchana, chhāra
āpane mānabi sadā chhāḍi’ ahaṅkāra 
chhāḍi’–Give up [your] ahaṅkāra–false ego, [and] sadā–always mānabi–consider āpane–yourself hīna–lower adhika–than tṛṇa–grass, dīna–poor, akiñchana–needy, [and] chhāra–mean. 
Give up your false ego, and always consider yourself lower than grass, poor, needy, and mean.
vṛkṣa-sama kṣamā-guṇa karabi sādhana
pratihiṁsā tyaji’ anye karabi pālana 
sādhana karabi–Practise guṇa–the quality kṣamā–of tolerance sama–like vṛkṣa–a tree. tyaji’–Give up pratihiṁsā–vengeance [and] pālana karabi–nurture anye–others. 
Practise tolerance like a tree. Give up vengeance and nurture others.
jīvana-nirvāhe āne udvega nā dibe
para-upakāre nija-sukha pāsaribe 
dibe nā–Do not cause udvega–anxiety āne–to others jīvana-nirvāhe–for the maintenance of [your] life, [and] pāsaribe–forget [your] nija–own sukha–happiness upakāre–in the course of helping para–others. 
Do not trouble others for your own upkeep, and forget your own happiness in the course of helping others.
ha-ileo sarva-guṇe guṇī mahāśaya
pratiṣṭhāśā chhāḍi’ kara amānī hṛdaya 
ha-ileo–Even if you are mahāśaya–honourable [and] guṇī–qualified [with] sarva–all guṇe–qualities, chhāḍi’–give up āśā–desire pratiṣṭhā–for prestige [and] kara–make [your] hṛdaya–heart amānī–prideless. 
Even if you are honourable and qualified with all qualities, give up desire for prestige and make heart your prideless.
kṛṣṇa-adhiṣṭhāna sarva-jīve jāni’ sadā
karabi sammāna sabe ādare sarvadā 
jāni’–Knowing [that] sarva–every jīve–soul [is] sadā–eternally adhiṣṭhāna–an abode kṛṣṇa–of Kṛṣṇa, sarvadā–always ādare–respectfully sammāna karabi–honour sabe–everyone. 
Knowing Kṛṣṇa resides eternally within every soul, always respectfully honour everyone.
dainya, dayā, anye māna, pratiṣṭhā-varjana
chāri guṇe guṇī hai’ karaha kīrtana 
dainya–Humility, dayā–compassion, māna–honouring anye–others, [and] varjana–giving up pratiṣṭhā–prestige— hai’–become guṇī–qualified [with these] chāri–four guṇe–qualities [and] kīrtana karaha–chant. 
Humility, compassion, honouring others, and giving up prestige—become qualified with these four qualities and chant the Name.
bhakati-vinoda kā̐di’ bale prabhu-pāya
“heno adhikāra kabe dibe he amāya” 
kā̐di’–Crying pāya–at the feet prabhu–of the Lord, bhakati-vinoda–Bhakti Vinod bale–says, “he–“O kabe–when dibe–will You give amāya–me hena–these adhikāra”–qualifications?” 
Crying at the feet of the Lord, Bhakti Vinod says, “O when will You give me these qualifications?”