Let's now see the philosophy of vishista advaita in brief. It wouldn't be wrong to say that this is the first of the entire set of vaishnava vedanta philosophies. The main propounder of this philosophy is Ramanuja. Ramanuja did study under an advaita guru but deviated and hence the birth of the new system.
This system tries to merge vaishnava philosophy with vedanta. It is but a fact that before Ramanuja and Bhaskara, there was only the system of Advaita propagated by Sankara. Ramanuja does mention about getting the commentary of Bodhaayana on the Brahma Sutras but the copy Ramanuja got was a mutilated one and it is also tough to trace out the same as Ramanuja doesn't give many quotations from that vritti in his Sri Bhashya. So as to this system being traditional and followed from time immemorial, it is under doubt and cannot be concluded.
The vishista advaita system bases itself mainly on the Sri Bhashya, the magnum opus of Ramanuja. Other important authors in this school are Vedanta Desika, Sudarshana Suri whose sub commentary srutha prakashika on the Sri Bhashya was preserved by Vedanta Desika and ranga ramanuja who wrote the upanishad bhashyas.
Ramanuja hasn't commented on the upanishads but he has discussed many upanishad vakyas in his sri bhashya. For upanishads, we do have the commentary of ranga ramanuja.
The basic philosophy of Vishista advaita is thus:
There are three distinct entities: Jeeva - the various individual beings who are associated with a particular body-mind complex, jada - the insentient entities in the world and Ishwara - creator, protector who is Vishnu and termed in scriptures as Brahman.
The Brahman of vishista advaita is not formless and partless, instead he has the parts of jeevas and jadaas. Vishnu's body is made up of jeevas and jadaas - thus the relation between jeeva-jada & Vishnu is that of Shareera shareeri bhaava. The way to realize is to surrender totally unto Vishnu which is termed as prapatti.
Vedanta in general speaks about four types of mukthi or moksha:
1. Salokya - getting the loka of the Lord
2. Sameepya - getting near the Lord as his servant
3. Saroopya - getting the same form as that of the Lord
4. Sayujya - merging into the Lord
Vishistadvaita believes in sameepya mukthi or getting close to Vishnu in Vaikunta. The jeeva can never become the Lord because he is different from the Lord and he is just a part of the Lord.
Thus the advaitic sruthi statements are with respect to the Lord as a whole & the dvaitic statements are with respect to the jeevas-jadas. Thus both are true. Vishistadvaita believes that it is only by their system that there can be true justice to all sruthi statements (both advaitic and dvaitic).
Since Brahman is qualified by jeevas and jadas, therefore this system is termed as Vishista advaita. Brahman is not nirguna but possesses infinite gunas.
To sum up:
1. Brahman is Vishnu
2. Vishnu has parts of jeevas and jadas
3. Mukthi is being near to vishnu and doing service to him
4. Mukthi is achieved through prapatti or surrender