Apart from understanding the relationship between Ātman and Brahman, I'm also interested in the prescribed techniques & modes of realising and sustaining this understanding. please assume no access to qualified Guru.
According to Vishista advaita, individual atmas are many in number, and have a sarira-sariri relationship with the Supreme Brahman. (yasya atma sariram - To whom atma forms the body - Subala Upanishad/Brhadaranyaka Upanishad). The Supreme Lord is still advaita, i.e., one without a second, but what makes Him visishta is He is present along with the prakruti and atmas as His body. He is the sariri, or the possessor and the individual atmas and prakruti form His body (sarira). This relationship is called seshatva-jnanam, or knowledge of being the sesha (part) of the seshi (whole).
The prescribed techniques and modes of realizing seshatvam and sustaining this understanding are stated in the Bhagavad Gita. Two popular techniques for realizing this are karma yoga and jnana yoga, and of the two, Krishna favors karma yoga since it is more practical for one who is conditioned to work in a specific way. According to the karma yoga, one must perform one's prescribed duties according to the Vedic injunctions. Such performance should be devoid of three conceptions - that you are the proprietor (sanga), that you are the controller (kartrutva), and that you are the enjoyer of that work (phala). The work should be done simply as a worship of the Supreme Person with the understanding that the injunctions enjoined in the scriptures to different people are His will and by enacting His will, He will be pleased. By this, the Supreme Brahman will be pleased and He will free one from previous sins which stand in the way of sustaining this understanding. By such annulling of sins, one's mind becomes peaceful. Once the mind becomes peaceful, the senses will be controlled. In such a state of mind, it is possible to get to the stage of sthita-prajnata or sustained understanding of this relationship. (This is the essence of the second and third chapters of Bhagavad Gita). To develop further however, one must advance into bhakti yoga, for, only by bhakti one can reach the Supreme. There are also Sampradaya specific ways, for instance, just chanting certain mantras can help one realize this and sustain this understanding, and for knowing these, one should approach a Guru. Any other way of knowing these may not give good results.
So from what I understand there are 3 major schools of Vedanta: Advaita (pantheistic), Vishistadvaita (panentheistic), and Dvaitadvaita (dualistic).
In the past I have researched Advaita-Vedanta but recently I've become interested in learning more about Vishistadvaita, for I've always been pretty drawn to "panentheistic" philosophies, and Vishistadvaita sounds very panentheistic to me - The Universe exists in Ishvara and Ishvara in the Universe (Atman), but ultimately Ishvara transcends the Universe as well. The whole is greater than the sum of its parts. Vishistadvaita seems like a "middle ground" between Advaita (everything is literally pure Brahman), and the dualism of Dvadiata. By the way, please correct me if anything I've said is wrong.
God has two modes of being, as cause and as product. As cause, he is in his essence qualified only by his perfections. As product, he has as his body the souls and the phenomenal world. There is a pulsating rhythm in his periods of creation and absorption. For Ramanuja, release (moksha) is not a negative separation from transmigration, or a series of rebirths, but rather the joy of the contemplation of God. This joy is attained by a life of exclusive devotion (bhakti) to God, singing his praise, performing adulatory acts in temple and private worship, and constantly dwelling on his perfections. In return, God will offer his grace, which will assist the devotee in gaining release.
Vishishtadvaita flourished after Ramanuja, but a schism developed over the importance of God’s grace. For the northern, Sanskrit-using school, known as the Vadakalai (“Monkey”) school, God’s grace in gaining release is important, but a human individual should make the best possible effort, as a baby monkey must hold fast to its mother. This school is represented by the thinker Venkatanatha, who was known by the honorific name of Vedantadeshika (“Teacher of Vedanta”).
Well, you should start off with the Sri Bhasya by Ramanuja. If you want to get into a little bit of Visishtadvaitic theology, you should read the BG commentary by Ramanuja as well.
These are the references I can give for books.
Brahman alone exists, but is characterized by multiplicity - is the key concept of qualified dualism.
Ishvara (denoted by Vishnu-Narayana) is the Supreme Cosmic Spirit who maintains complete control over the Universe and all the sentient beings, which together also form the pan-organistic body of Ishvara. The triad of Ishvara along with the universe and the sentient beings is Brahman, which signifies the completeness of existence. Ishvara is Parabrahman endowed with innumerable auspicious qualities (Kalyana Gunas).
Shukla Yajur Veda 32.3
Ishvara is perfect, omniscient, omnipresent, incorporeal, independent, the creator of the universe, its active ruler and also its eventual destroyer.
He is causeless, eternal and unchangeable — and is yet the material and the efficient cause of the universe and sentient beings. He is both immanent (like whiteness in milk) and transcendent (like a watch-maker independent of a watch). He is the subject of worship. He is the basis of morality and giver of the fruits of one's Karma. He rules the world with His Maya — His divine power.
Brihadaranyaka Upanishad 3.7.4-14
He who inhabits water, yet is within water, whom water does not know, whose body water is and who controls water from within - He is your Self, the Inner Controller, the Immortal.
He who inhabits the sun, yet is within the sun, whom the sun does not know, whose body the sun is and who controls the sun from within - He is your Self, the Inner Controller, the Immortal.
Chit is the world of sentient beings, or of entities possessing consciousness. It is similar to the Purusha of Samkhya system. The sentient beings are called Jīvās and they are possessors of individual consciousness as denoted by "I". The scope of Chit refers to all beings with an "I" consciousness, or more specifically self-awareness. Therefore, all entities which are aware of their own individual existence are denoted as chit. This is called Dharmi-jnana or substantive consciousness. The sentient beings also possess varying levels of Dharma-bhuta-jnana or attributive consciousness
The jivas possess three different types of existence:
Nityas, or the eternally free Jivas who were never in Samsara.
Muktas, or the Jivas that were once in Samsara but are free.
Baddhas, or the Jivas which are still in Samsara