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

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]

Mantras and Vrat for Praayashchit
[Agni Puraan, Ch 171, p 343-344]

Pushkar Jee said to Parashuraam Jee - "Now I tell you about the Praayashchit of Gupt (secret, or hidden) sins.

(1) Who does Jaap of Purush Sookt for one month, his all Paap are washed away.

(2) Aghamarshan Mantra Jaap frees from all kinds of sins.

(3) Ved Mantra, Vaayu Sookt, Yam Sookt, and Gaayatree Mantra Jap washes all sins of the persxon.

(4) 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.

(5) If a man takes only 8 morsels food for 1 month - it is called "Yati Chaandraayan" Vrat.

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

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

(8) 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. And if somebody drinks the same things cold in the same sequence - it is called "Sheet Krichchhra" Vrat.

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

(10) 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 - it is called "Krichchhra Saantapan" Vrat.

(11) If the above things are taken one by one each day - it is called "Mahaa Saantapan" Vrat.

(12) And if the same things are taken one by one for 3 days each - it is called "Ati Saantpan" Vrat.

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

(14) 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.

(15) If only one part of this Vrat (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.

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

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

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

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

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

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

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

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

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

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

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

(27) If somebody eats only sesame seeds (Til) for 12 days - it is called "Aagneya Krichchhra" Vrat. This Vrat removes all sorrows.

(28) Take one Pasar Laaj (Kheel or puffed rice) 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.

Whoever worships Devtaa and does Krichchhra Vrat with the desire of wealth, health, Swarg and destroying the sins, he attains everything.