What Happens on Moksha?

My sources for this answer includes specific works of Adi Shankara and Swami Ramanuja (even though they are from two different schools, they seem to have agreed on this aspect). Since we are discussing about moksha I am only going to discuss here what happens from the time of death of the person who is about to attain moksha.  The sources for what I am going write includes a scripture called archiradi gati, Swami Ramanuja's sharanagati gadyam, and verses form Thiruvaimozhi by Swami Nammazhwar (Part of 4000 diva prabandham, the tamil vedas, practiced as vedas in south indian temples called divya-desams), Adi Shankara's Sri Ranganatha Stotram.

Firstly, Mind is matter (a sookshma sharira, but a sharira nevertheless). When the body falls (when the person dies), the Aatma does a visarjan (gives up) of the sthoola (physical) and sookshma (subtle) sharira (bodies).  AT that instant (when the visarjan is taking place) the knowledge of "Swaroopa" dawns on the Jeevatma. Swaroopa Jnana means, what is the Jeevatma in relation to the Paramatma.  Thereafter, the Vishnudhootas take the Jeevatma that going to attain Moksha to the Vishnu-loka or Parama Pada or Sri Vikuntha as it is called. The Path thus taken to Sri Vaikuntha is called "Archiradi Marga".  It is an exclusive path for those Jeevatmas that attain Moksha.  Those that do not attain Moksha leave by a path called as "Dhoomati Marga", the destination of which is Yama Loka.  There is another Path taken by Sanyasins (i dont know the name of the route) - but they reach Indra-Loka (Sanyasins do not fall in Yama's Jurisdiction).

Enroute on the Archiradi Marga, the Jeevatma passes through a number of deva-lokas - including Indra's world, Varuna's world, and even Brahma's Satya Loka.  Even though all of them invite the Jeevatma to visit them, the Jeevatma is in a hurry to get its Moksha and politely declines these invitations to go on to Sri Vaikuntha.

At Sri Vaikuntha, before it enters, there is a river called the "Viraja River".  The Jeevatma takes a dip in the Viraja River.  When it comes out after taking a dip, it acquires a new "Sharira".  The difference between the sharira we have on earth and the Sharira we take on in the Sri Vaikuntha is in the "gunas".  On earth, our shariras (and everything in nature) is composed of the gunas of Sattva, Rajas, and Tamas.  However, the Sharira we take on in Sri Vaikuntha is composed of "Shudda Sattva" guna.  For that reason it is called "Diva-Mangala-Vigraham". (A beautiful/excellent sharira, if you will).  Sattva Guna's primary characterisic is "knowledge" (Yathavasthita Jnana). In that Sharira is acquires God-like qualities and attains equanimity with the Brahman in "ananada" or Happniess.  That is the reason why the shastras say that the Jeevatma acquires "Samyapatti" with the Brahman.  At no time, does it ever merge with or becomes the Brahman.  It also acquires 6 Kalyana Gunas that describe the word "Bhagwan" - Bha stands for two gunas - Gnana (Knoweldge) and Bala (Strength), Ga stands for Aishwarya (Ability to command over everything) and Veerya (Ability to remain without change), Va stands for Shakti (Being the material cause of everything) and Tejas (Ability to remain independent not needing anybody or anything's help to achieve its goals).

In addition, the Jeevatma acquires the qualities of Satyasankalpatvam and Satyakamatvam. It is now able to go to any loka of its choice, meet anyone of its choice, take any shape it wants.   It acquires its own "shanka" and "chakra" and takes on the four handed form that we see Maha-vishnu in.

There is a reception now organized for the Jeevatma after it has acquired this Sharira.  The Jeevatma is taken to its quarters, and decorated by beautiful apsaras. The Jeevatma even gets a wife.  Elders who are known to the Jeevatma that have attained Moksha welcomes it.  All of them together take the Jeevatma to meet the Lord Sriman Narayana, the Formful Brahman.  There the Jeevtma goes reciting Annasooktam (basically ahamannan ahamannam ahamannado ...etc.) The Lord embraces the Jeevatma and asks it "what took you so long to reach me".  The Jeevatma is like a child in front of the Lord.  The plays with it a while.  Sri Mahalakshmi the Lord's consort is also the leader of the Jeevatmas.  She assigns the service duties to the Jeevatma.  Thus the Jeevatma becomes a Legal Permanent Resident/Citizen of the Sri Vaikuntha.  No passport, No visas, and No Border Protection Officials asking stupid questions.

Note: There is another state called Kaivalya - attained by those that are consumed by "self-realization".  They also attain Moksha.  However, since they are enjoyers of the "Atma-Swaroopam" they remain enjoying their own self outside the Viraja river.  They do not acquire the divya-mangala-vigraham or the excellent body.