I hope the following answer conveys the idea of why it is non trivial to answer your question briefly. Your question is akin to asking "What is the procedure to worship the Lord" or "What is the procedure to perform Sandhyavandana". Nothing short of an elaborate manual would suffice to answer your question. I hope the linked videos of Agnihotra practice demonstrate this.
There is a lot of incorrect information being spread about Agnihotra. Much of what can be found on the internet or YouTube about Agnihotra on neo-Hindu websites is pure fiction.
It is incorrect that it is simple/easy to perform Agnihotra (well, simple/easy is a perspective). It is also incorrect that anyone and everyone can perform Agnihotra. Agnihotra is a Vedic ceremony/lifestyle and thus comes with all rules/eligibility criteria that Vedic yajnas do. For an example of Agnihotra in Shukla Yajur Veda see the recording of Ram Prasad Gautam of Nepal. For an example of Agnihotra in Krishna Yajur Veda, see this video and related recordings of the fortnighly sacrifices.
I am going to describe Agnihotra in the context of Brahmin performers. It is possible that Kshatriyas and Vaishyas also are eligible to perform it, but I only know about the eligibility of Brahmins.
A Brahmin student after completing his basic Vedic education (learning to recite the text of his own recension/shakha) tend specialize one of the following paths:
- further studies in Vedic recitation (advanced modes of recitation like Krama and Ghana),
- further studies in one or more Sastras: Tarka, Vyakarana, Mimamsa, Vedanta, Dharma texts, Agama, Veda Bhashya
- further studies in Grihya Sutras and the performance of upAdhyAya or paurohitya (performing domestic rituals for families).
- further studies in Mimamsa/Srauta followed by a commitment to the lifelong performance of Agnihotra.
These four paths are not mutually exclusive. E.g. one can learn advanced Vedic recitation, learn Tarka Sastra and perform Agnihotra while also being a family priest. However it is not typical for people to do so.
There are other eligibility criteria to pursue the path of Agnihotra. E.g. One must be married with a living wife (the ceremony is jointly performed) and must have a son (jAta-putraH). His hair must still be predominantly black (kRRiShNakeshI).
jātaputraḥ kṛṣṇakeśī agnīnādadhīta (śabara on jaiminī 1.3.2-3)
He must either be an eldest son, OR his older brothers must all be practising Agnihotrins, OR he must receive permission from his older brothers to kindle his fires before them.
Agnihotra is performed in three fires: Garhaptya, Ahavaniya and Dakshinagni. The setting up the the three fires is performed in a ritual called agnyAdhAna. Once lit, the fires must not burn out until the sacrificer, or his wife dies. In practice, the Dharma Sastras allow some flexibility about this for exceptional circumstances, OR old age.
Performing daily agnihotra is accompanied by the fortnightly, monthly and quarterly yajnas. Having performed this for one year, the performer becomes eligible to perform advanced Vedic Yajnas like the Seven Soma sacrifices.
I would guess that there are less than one hundred living performers of traditional Agnihotra today! Some Kalivarjya texts prohibit the performance of the Agnihotra in the Kali Yuga.
- David Knipe's monograph - "Vedic Voices: Intimate Narratives of a Living Andhra Tradition"
- The 'Kalivarjyas' or 'Prohibitions in the Kali Age' by Batuknath Bhattacharya.