What is misogi?
Misogi is any of a number of purification rituals found in shinto, the most common of which is misogi shuho or misogi-no-gawa, a purification ritual of cleansing the body in a river.
To be somewhat precise, the kami ("spirit-god" for lack of a better description) who created the Solar System and the ancestor of all kami on Earth, Izanagi-no-Okami) visited yomi (the world of the dead) and, upon emerging, performed the first misogi shuho to cleanse his body of the defilement of that world. In doing so, he first cast all his belongings into the river, then himself, and from all his belongings, from his eyes, and from his nose, came the other kami. (I am, of course, overly simplifying this because I doubt you care which kami sprung from which orifice).
This misogi shuho has 6 elements:
- To purify yourself from attachments
- Self reflection
- To find the middle way
- To check constantly and correct thoroughly
- Inner willingness and sincere effort
Another ritual common among aikidoka is something called misogi-no-kokyu-ho or purification of spiritual refinement. This is an arduous form of directed meditation, restricted diet, and imposed asceticism, the first experience of which is four days long.
Are there techniques that this can be done[?]
Yes. It's an extremely shinto concept, and Ueshiba Morihei was part of a shinto cult called Omoto-kyo (I use the term "cult" to imply a non-mainstream religious sect, not to imply anything else – some people get touchy about this word).
In the four day shogaku shugyo of misogi-no-kokyu-ho, the student wears gi and hakama; eat 3 meals a day consisting of a barley-rice mixture, soybean paste, salted plum (umeboshi), and radish pickles (takuan); and sleep on tatami mats. For those four days, the students sit in seiza, practice breathing techniques, and chant from their hara (abdomen). This is an intensive; a practice of deep commitment to push the aspirant hard.
In the misogi-no-gawa, the aspirants strip down to fundoshi (loincloth) and hachimaki (headband), and sit in meditation for a time. Then they are led through a river to a waterfall, where they stand in meditation and self-reflection, performing a chant (misagi- no-Oharai) under a waterfall.
[W]hat is the actual effect on the person?
These are rituals, and, like all rituals, the actual effects will vary from person to person based on the meaning they ascribe to them. Ueshiba Morihei's epiphanies at different times in his life were an understanding of his martial art as an expression of his spiritual beliefs.
If you ascribe no personal beliefs to the practices, they will be shallow, rote motions and have no gain. In this case, the best one can hope for is a capacity to sit in seiza and breathe, or, in the case of misogi shuho, a resistance to icy cold water.
However, if you take the time to ascribe a belief to what you will get out of something, and that belief is reasonable ("I will emerge with a cleared perspective of the world," not "I'm going to come out of the water to find $50 on the ground."), it will have that effect upon you.