PURIFICATION

Alternative or 'Other' Kalachakra refers to the path of the Kalachakra practice and is traditionally divided into the Initiation, the Generation Stage Practice and the Completion Stage Practice.
All other Maha-Annutara Tantras describe three practices: transforming death into the Dharmakaya, bardo into the Sambhogakaya and rebirth into the Nirmanakaya. In Kalachakra however, there is no separate description of transforming the bardo into the Sambhogakaya. The bardo is considered similar to rebirth and they are taken as one; so it describes just transforming death into the Dharmakaya and rebirth into the Nirmanakaya.
The Basis for purification is the form aggregate (or the elements), the Path is the two stages (Generation and Completion Stage) and the Result is the two bodies of a Buddha: Dharmakaya and Rupakaya. See also [1] for a description of differences in practice between Guhyasamaja and Kalachakra.

GENERATION STAGE

Traditionally, one practices some daily meditations after receiving the Kalachakra initiation.

Within the Gelug tradition, one is instructed to daily practice the "6-Session Guru Yoga" in order to keep to one's tantric commitments that come with every Highest Yoga Tantra initiation. Texts for this practice exist in various lengths (even just a four-line version is available when in haste) and some are dedicated to specific tantric deities.
When His Holiness the Dalai Lama gives the initiation to Westerners, he does not commit them to do the specific "Kalachakra 6-Session Guru Yoga", although the commitment to do this relatively long practice at least once daily is often given to Tibetans during the initiation.  The text of this and other practices can be found via the Resource Page.

Below explanation refers not specifically to the Six-Session Guru Yoga, but to the main other sadhanas.

Referring to the main Gelugpa Body, Speech and Mind Mandala Sadhanas as found in the Resource Page:

[5]: When we subdivide the generation stage meditations, they are said to be twofold.
Firstly there is the process of meditation on how at the time of death the bodily elements withdraw and the clear light of death arises; to symbolize this, one intensifies one's accumulation of meritorious energy and contemplates the four doors of liberation.
Secondly, to symbolize the process of crossing through the intermediate stage and entering into a womb of rebirth, there is the yoga of meditating upon the four branches of approach and accomplishment. This second phase involves the four following (visualized) processes in the sadhana:

1. "Approximation", called the "Supreme Royal Mandala"
2. "Approximating accomplishment", called the "Supreme Royal Actions"
3. "Accomplishment", called the "Drop Yoga"
4. "Subtle Yoga"

These four branches lay the basis for respectively, the Kalachakra Vajra-Body; the Kalachakra Vajra-Speech; the Kalachakra Vajra-Mind and the Kalachakra Vajra-Exalted Wisdom. The first two branches are generation stage practices, the last two are completion stage practices. The contemplation of the four joys in the generation stage is actually a simulation of the genuinely transformative experience of them that will occur during the Completion Stage. One does not, in the generation stage, actually uproot defilements or directly cognizes emptiness; one does, however, lay a powerful basis for those attainments.

During the meditation on the sadhana, one visualizes oneself as both Kalachakra and Vishvamata, surrounded by the mandala as the enlightened aspects of oneself, the universe and the practice. Various different sadhanas of Kalachakra exist, but only the longer ones are suitable for an 'Approximation retreat', which qualifies the practitioner to perform various rituals like 'Self-initiation'. The minimum practice for such a retreat is the Mind Mandala sadhana, which easily takes 2 hours or more to complete.
During an approximation retreat one does daily meditations and the recitation of hundreds of thousands of mantras. When these are completed (possible in about 6 to 8 weeks), a purifying fire puja is to be done to complete a full approximation retreat, which qualifies one to do e.g. self-initiation. Longer retreat versions can be the 3-year retreat, or simply the rest of one's life, until one achieves a very high level of concentration and identification with the deity.

It is said that when one can hold the visualization of the complete mandala including all its 722 deities in all detail for prolonged time in a very small drop, one is ready for the next step; the 'Completion Stage', in which the actual transformation into the deity takes place.

BIBLIOGRAPHY

[1]: Highest Yoga Tantra, Daniel Cozort, Snowlion 1986
[2]: The Kalachakra Tantra, Rite of Initiation. Tenzin Gyatso the Dalai Lama and Jeffrey Hopkins (Wisdom, 1985)
[3]: Taking the Kalachakra Initiation, Alexander Berzin, Snow Lion, 1997 ISBN 1-55939-084-0
[4]: Transcending Time, An Explanation of the Kalachakra Six-Session Guru Yoga, Gen Lamrimpa and B. Allan Wallace (Wisdom 1999) ISBN 0-86171-152-1
[5]: The Practice of Kalachakra by Glen H. Mullin (Snow Lion 1991)
[6]: Introduction to Kalachakra, commentary by Dr. Alex Berzin June 28 - 30, 1985 at Institut Vajrayogini, France
[7]: Das Mandala by Martin Brauen (Dumont 1992) (Later appeared in many languages.)
[8]: The Wheel of Time Sand Mandala, by Barry Bryant, Harper Collins 1995, ISBN 0-06-250088-0