Types of Fasts
There are three types of Vrat according to the time of taking food. 

(1) Ek-Bhukt Vrat - In this Vrat people eat only once in the evening just after sunset and do not eat
       until next sunrise..
(2) Nakt Vrat - In this Vrat people eat only once in the night and do not eat until next sunrise.
(3) A-Yaachit Vrat - In this Vrat one eats whatever food he has got, he does not ask for it.

Saantapan Vrat
In this Vrat a mixture of cow's urine, cow's dung, cow's milk, cow's yogurt, cow's Ghee, and cow's Kush water is drunk only once on one day, and then the next day one does not eat anything for 24 hours. This is 2-day Saantapan Vrat.

Mahaa-Saantapan Vrat or Krichchhra Vrat
If the above mentioned six things are taken separately, one on each a day, and then the fast is kept on the 7th day for 24 hours, it is called Mahaa-Saantapan Vrat.

Ati-Krichchhra Vrat
In this Vrat one eats one morsel, once only in the morning for three days; once only in the evening for three days; and once only without asking (A-Yaachit) for three days, then in the end keep complete fast for three days. This is called Ati-Krichchhra Vrat.

Chaandraayan Vrat
Chaandraayan Vrat is of two types - one is done by increasing the food intake, and another is done by decreasing the food intake. One should take 15 morsels of food on Poornimaa after taking bath three times - in the morning, afternoon and evening. Then from Krishn Pratipadaa, one morsel food should be decreased each day until on Chaturdashee day when one takes only one morsel food. Keep complete fast on Amaavasyaa, and then increase one morsel food each day until Poornimaa when one eats 15 morsels of food again. This is of one type. In the other type, the process is reversed - starting from Amaavasyaa and ending on Amaavasyaa - first increasing then decreasing. [This comes to 240 morsels food in one month)
[Bhavishya Puraan, 1/20]

Chaandraayan Vrat is of three types - Yav-Madhya, Pipeelikaa-Madhya, and Shishu-Chaandraayan. (1) In Yav-Madhya, this Vrat is started from Shukla Paksh Pratipadaa, eating one morsel increasing to 15 morsels till Poornimaa, then decreasing one morsel each subsequent day till Amaavasyaa. End it on Amaavasyaa. (2) In Pipeelikaa-Madhya, this Vrat, is started on Poornimaa by eating 15 morsels, then decreasing one by one morsel, keep fast on Amaavasyaa, then increase one by one morsel till next Poornimaa. (3) In Shishu or General Vrat, the Vratee takes 8 morsels each day for 30 days, thus they add to 240 morsels in one month.
[Bhavishya Puraan, p 183]

Before beginning of these rites, one has to shave and give Daan and Dakshinaa to Braahman.
According Paraashar Smriti "A man who has relations with other women than his wife, can get purified only by observing Chaandraayan Vrat (a fast devoted to the Moon), so such relations were there even during Paraashar's period.

Praajaapatya (Praajaapatya Krichchhra) Vrat
In this Vrat one eats food once only in the morning for three days; once only in the evening for three days; and once only without asking (A-Yaachit) for three days, then in the end keep complete fast for three days - doing it for totaling 12 days. This is called Praajaapatya Vrat.
[Padm Puraan, p 401-402]

Paarak Vrat
Whatever Vrat is completed in 12 days, it is called "Paraak" Vrat - this destroys all sins.
When the same Vrat is completed in 36 days (in 3 times time of Paarak Vrat), it is called "Mahaa Paraak".

Variations of Chaandraayan, Krichchhra and Santaapan Vrat
In all Krichchhra Vrat one should not shave head, take bath, do Havan and worship Hari. Whoever is doing Krichchhra Vrat, if he stands in the day time, and sit in the night time, it is called "Veeraasan". A Man becomes sinless by doing this Vrat.

Rishi Chaandraayan - Taking three handful of food for one month and living a life of austerity is called "Rishi Chaandraayan".

Shishu Chaandraayan - If a man takes 4 morsels food in the morning and 4 morsels food in the evening leading a proper life for 1 month - it is called "Shishu Chaandraayan" Vrat.

Sur Chaandraayan - If somebody takes 240 Pind (morsels) in any way in 1 month (8 morsels a day) - this is the method of " Sur Chaandraayan" Vrat.

Yati Chaandraayan - If a man takes only 8 morsels food for 1 month - it is called "Yati Chaandraayan" Vrat.
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Ati Saantapan - And if the cow's urine, cow dung, cow's milk, cow's yogurt, cow's Ghee and Kush-water  are taken one by one for 3 days each 15-days Vrat) - it is called "Ati Saantpan" Vrat.

Krichchhra Saantapan - If one lives by taking cow's urine, cow dung, cow's milk, cow's yogurt, cow's Ghee and Kush-water one day and keep complete fast the second day (2-days Vrat) - it is called "Krichchhra Saantapan" Vrat.

Mahaa Saantapan - If the cow's urine, cow dung, cow's milk, cow's yogurt, cow's Ghee and Kush-water are taken one by one each day (5 days Vrat) - it is called "Mahaa Saantapan" Vrat.
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Aagneya Krichchhra - If somebody eats only sesame seeds (Til) for 12 days - it is called "Aagneya Krichchhra" Vrat. This Vrat removes all sorrows.

Aamalak Krichchhra - When only Aamalaa fruit is eaten for 1 month - it is called "Aamalak Krichchhra" Vrat.

Aghmarshan Krichchhra - Reciting Aghamarshan Sookt followed by Trishavas Snaan and observing fast for three days is called Aghamarshan Krichchhra.

Ardh Krichchhra - This consists of taking food for one day in day time only, followed by one day food at night time only, followed by two days at one time food available without begging (A-Yaachit) and two days of starvation. This takes a total period of 6 days to complete. It is called "Ardh Krichhra" Vrat.

Dadhi Krichchhra - When only yogurt is eaten for 1 month - it is called "Dadhi Krichchhra" Vrat.

Dugdh Krichchhra - When only milk is taken for 1 month - it is called "Dugdh Krichchhra" Vrat.

Jal Krichchhra - When only water is taken for 1 month - it is called "Jal Krichchhra" Vrat.

Krichchhraati Krichchhra - If somebody takes only milk for 21 days - it is called "Krichchhraati-Krichchhra" Vrat.

Krichchhrapaad - If one takes food 3 days in the morning, or 3 days in the evening, or 3 days without asked food ( A-Yaachit), or keeping complete fast in the last 3 days is done - it is called "Krichchhrapaad" Vrat. Same as Praajaapaty Vrat given below.

Mool Krichchhra - When only Mool (roots) is eaten for 1 month - it is called "Mool Krichchhra" Vrat.

Paarak Krichchhra - If somebody lives without eating for 12 days - it is called "Paraak Krichchhra" Vrat.

Pad Krichchhra - (One quarter) If somebody takes food for one day in day time only, followed by one day food at night time only, followed by one day at one time only available without begging (A-Yaachit) and one day of starvation. This takes a period of 4 days to complete - it is called "Pad Krichhra" Vrat.

Padmaaksh Krichchhra - When only Padmaaksh (Kamalgattaa) fruit is eaten for 1 month - it is called "Padmaaksh Krichchhra" Vrat.

Patra Krichchhra - When only leaves are eaten for 1 month - it is called "Patra Krichchhra" Vrat.

Phal Krichchhra - When only fruits are eaten for 1 month - it is called "Phal Krichchhra" Vrat.

Pushp krichchhra - When only flower is eaten for 1 month - it is called "Pushp Krichchhra" Vrat.

Sheet Krichchhra - And if somebody drinks the cold water for 3 days, cold milk for 3 days, and cold Ghee for 3 days - it is called "Sheet Krichchhra" Vrat.

Shree Krichchhra - When only Bel fruit is eaten for 1 month - it is called "Shree Krichchhra" Vrat.

Tapt Krichchhra - If somebody drinks warm water for 3 days, warm milk for 3 days, warm Ghee for 3 days and Vaayu (air) for 3 days - it is called "Tapt Krichchhra" Vrat.

Vaayavya Krichchhra - When only one Anjuli (whatever fits in one hand) food is taken for 1 month - it is called "Vaayavya Krichchhra" Vrat.

Yavak Krichchhra - Taking gruel of barley for one month is called "Yavak krichchhra" Vrat.
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Brahm Koorch - Take one Pasar Laaj (means Kheel or puffed rice - Mamra or Murmuraa) everyday for 13 days, and keep complete fast on 14th and Amaavasyaa or Poornimaa; then eat food of Havishya Ann after drinking Panchgavya. This Vrat is called "Brahm Koorch" Vrat. If somebody does this Vrat 2 times in 1 month, he gets freed from all kinds of sins.
Pasar = a hollow place by joining both hands from the front part of the smallest fingers to the end part of the palm
Laaj = Kheel. Kheel is roasted Dhaan (rice with husk). Or alternatively called Murmuraa, Mamraa, means roasted rice (without husk)
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Praajaapatya - If somebody eats for 3 days in the morning, 3 days in the evening, 3 days without asked food (A-Yaachit) and keep complete fast in the last 3 days - it is called "Praajaapatya" Vrat - same as Krichchhrapaad Vrat given above. Whoever worships Devtaa and does Krichchhra Vrat with the desire of wealth, health, Swarg and destroying the sins, he attains everything.

Alternative to Krichchhra Vrat
(1) Hemaadri says that because due to the change of time and place, we may not be able to observe Praajaapatya Krichchhra, some other alternatives have been prescribed by great sages. This Krichchra according to them is equivalent to feeding 12 Braahman or 10,000 times chanting of Gaayatree Mantra or doing 1000 Til Hom.
(2) Paraashar says that Praajaapatya Krichchhra is equivalent to 200 Praanaayaam; Or 12 times bathing in sacred rivers like Gangaa; Or Walking 20 miles singing the names of God Or Chanting Gaayatree Mantra 10,000 times
It is sufficient if one of them is observed.
(3) Madhaveeya says that if we are not able to observe Praajaapatya Krichchra Vrat, we have to give one
cow to a Braahman, If this is not possible, we can give sufficient money to buy a cow to a Braahman

If without intention sins occur to sagely elders, one can do Jap and Hom and get rid of the sin. If Sin is done by one who does not follow Aachaar, he has to do Krichchhra Vrat to get rid of sins. In case of rich people they can get rid of their sins by large donations of wealth.

All Sins Destroyer Stotra
[Agni Puraan, p 355]

Pushkar Jee said - "When people want to commit sins, they are benefited by prayers. At that time one should pray Him like thus (given on p 355 ). Who reads or listens to this Stotra he becomes free from all sins committed by mind, speech and actions and attains Vishnu Lok freeing himself from all Paap Graha. Therefore one should do Jap of this Stotra on committing any kind of sin. Who observe Krichchhra Vrat, it is good for them also. By doing Jap and Vrat all sins are destroyed, therefore to attain pleasure and Moksh, one should take up them."
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--Chaandraayan and Praajaapaty Vrat destroy sins.
--Soorya, Shiv, Shakti, Vishnu's Mantras Jap also destroy sins.
--Besides, Gaayatree, Pranav, and Paap Vinaashak Stotra also destroy sins.
--The Mantras of Soorya, Shiv, Shakti and Vishnu, which start from "k", with "Raa" Beej, Raadi etc and Raant Mantra give million times fruits.
--Besides, the Mantra which start from "Aum Kleem" Chaturthyant and end in "Namah" fulfill all desires.
--The Jap of 12-letter and 8-letter Mantra of Narasinh Bhagavaan destroys all sins.
--Reading Agni Puraan also destroys all sins.
1--0 types of gold Daan (donations), 12 types of Dhaanya (grains) Daan, Tulaa Purush etc 16 Mahaa Daan; and above all Ann (cooked or uncooked food) Daan - all these destroy sins.
--Daan given on Tithi (days of Lunar calendar), Vaar (Sunday, Monday etc), Nakshatra (Ashwinee, Maghaa, Pushya etc), Sankraanti (transition day for Sun from one zodiac sign to another), Yog (at the unity of two occasions), stating day of Manvantar, for the sake of Soorya, Shiv, Shakti and Vishnu - all destroy all sins.
--Daan given in Teerth also destroy sins.
[Agni Puraan, p 359-360]