Aatm Triteeyaa Vrat
Aatm Triteeyaa Vrat is done in Maargsheersh Maas (Agahan). In this Vrat, one should feed a Braahman after worshipping Paarvatee. Beginning with Maargsheersh 3rd, end the Vrat in Paush Maas and worship Paarvatee with these names respectively in 12 months - Gauree, Kaalee, Umaa, Bhadraa, Durgaa, Kaangti, Saraswatee, Vaishnavee, Lakshmee, Prakriti, Shivaa and Naaraayanee. One attains good fortune and Swarg by doing this Vrat.

Akshaya Triteeyaa
The Akshaya Triteeyaa comes in Vaishaakh Maas, Shukla Paksh. As its name is, whatever is done on this day is immortal or many many lives. So the care should be taken not to do any bad action on this day, rather do good he everybody including Vrat, Daan, reading scriptures, singing Bhagavaan's glory etc.

Damanak Triteeyaa Vrat
Damanak Triteeyaa Vrat is done in Chaitra Maas. In this Vrat one should worship Paarvatee with Damanak flowers.

Gauree Triteeyaa Vrat
Whoever woman desires all kinds of pleasures, she should take up Gauree Triteeyaa Vrat. She should not eat salt on that day. Whoever does this Vrat for the whole life, Gauree gives her beauty and Saubhaagya. Gauree herself told its method to Dharm Raaj. Gauree said - "Whoever woman does this Vrat she lives with her husband as happy as I live with Shiv. Maidens should do this Vrat to get a good husband. She should not eat salt on that day. Make a golden idol of Gauree and worship it. Offer various Naivedya to her. Take food without salt in the night and sleep there only near Gauree idol.

Whoever maiden observes this Vrat like this, she gets a good husband and enjoys all kinds of pleasures. If widow observes this Vrat she meets her husband in Swarg. Indraanee did this Vrat to get a son and she got Jayant. Arundhatee also did this Vrat that is why she can be seen with her husband Vashishth Jee. Rohinee did this Vrat to become the chief wife of Chandramaa. Triteeyaa of Vaishaakh, Bhaadrapad and Maagh months are better than the other ones; and among them also Bhaadrapad and Maagh months Triteeyaa give special fruits.
On Maagh Triteeyaa one should donate jaggery and salt. 
On Bhaadrapad Triteeyaa one should donate Pooaa made with jaggery; to please Shiv Jee, donate Laddoo and water on this day.

Saubhaagya Shayan Vrat
This is done on Lalitaa Triteeyaa - Chaitra Shukla 3rd. On this day Paarvatee Jee was married to Shiv Jee. Take bath with sesame seeds mixed water and worship Paaravtee saying "Namo Paatalaayai" and Shiv saying "Shivaaya Namah". The following flowers have been prescribed for Shiv worship from Chaitra month onward - Mallikaa, Ashok, Kamal, Kund, Tagar, Maalatee, Kadamb, Kaner, blue evergreen flower, Aanbolee, Kumkum, Sendhuvaar. Keep 8 Saubhaagya materials (Kesar, milk, Doorvaa, sugarcane, salt, and coriander etc). In the night sleep in the same room and next day feed a Braahman couple after worshipping Umaa Maheshwar and give those Saubhaagya materials to them saying "Lalitaa Preeyataam Mam".

This Vrat can be done on Vaishaakh, Bhaadrapad and Margsheersh Shukla Triteeyaa (3rd Day) also. During these months, one should worship Umaa with "Lalitaayai Namah". At the end of the Vrat, in each fortnight, one should worship a Braahman couple. Thus after worshipping them with 24 clothes, one attains pleasures and Moksh.

Another kind of "Saubhaagya Shayan Vrat" may be done on Shukla Triteeyaa of Phaalgun etc months. One should not eat salt in this Vrat. At the end of the Vrat, worship a Braahman couple saying "Bhavaanee Preeyataam" and donate all necessary things for a house. In the same way it should be done on Shukla 3rd of Vaishaakh, Bhaadrapad and Maagh.

Vaishaakh Triteeyaa
This Triteeyaa is a general one for all. On Vaishaakh Triteeyaa, one should donate sandalwood mixed water and Laddoo to please Brahmaa Jee. This is called Akshaya Triteeyaa (or Akshaya Teej). Whatever is donated on this day, it becomes immortal, and the donor goes to Soorya Lok."
[Bhavishya Puraan, 1/8]