What Kind of Worship is Done on This Day :
Akshaya Triteeya is known as one of the most three auspicious Muhoort in Hindu Astrology - Lakshmee Poojaa (Lakshmee Kuber Poojaa), Gauree Poojaa, and Chandan Poojaa to Lord Krishn are the main rituals on this day.

--Padmaavatee Poojaa - for mental peace, business and wealth
--Lord Vishnu - recite Vishnu Sahastra Naam.
--Perform simple Vishnu Pooja in the morning with Tulasee leaves and flowers.
--Tulasee water is sprinkled during Aaratee
--Fasts, charity, a dip in the Sacred Rivers like Gangaa are undertaken.
--Worship Lard Vaasudev with rice grains
--Offer barley in a sacred fire
--Offer Anna Daan to poor.
--Worship Lord Ganesh and Lakshmee on this day.
--Pray to one of the Asht Dikpaal - Shree Bhavan Kuber today.
--Perform Mahaa Lakshmee Anushthaan.
--Throw 4 Kaudees (shells or Cowries) in all 4 directions to attract wealth opportunities
--Perform Shatru Shaanti Anushthaan so that enemies never trouble again.
--Recite Anang Mantra Jaap to improve health and to reduce impotency problems
--Perform Sadaashiv Poojaa with Neem leaves, these leaves when placed under a sick man's pillow are
    believed to cure the illness.
--Recite Mahaa Mritunjaya Mantra or perform Rudra Havan.
--Offer barley preparations to your Isht Dev
--Offer Pohaa to Krishn just as Sudaamaa did
--Donate umbrellas, and sandals to poor.
--Perform Shree Yantra Poojaa since, the 6th incarnation of Vishnu Parashuraam brought Shree Vidyaa or Shree Yantra to the world today.
--Kuber Lakshmee Poojaa for Aishwarya Abhivriddhi - Kuber is the God of Wealth and the Guardian of North; Chanting of Kuber Mantra blesses the worshipper with money and prosperity by drawing new avenues and sources of income and wealth. Mantra of Kuber helps to increase the flow of funds and the ability to accumulate wealth. Kuber Mantra - 
-- "Om Sham Kuberaaya Namah"
-- "Om Hreem Shreem Hreem Kuberaaya Namah"
-- "Om Shreem Om Hreem Shreem Kleem Shreem Vitteshwaraaya Namah"
-- "Om Yakshaaya Kuberaaya Vaishravanaaya Dhana Dhanyaati Pataye
     Dhan Dhaanya Samriddhi me Dehi Tapaya Swaahaa"

The Poojaa starts in the morning and ends in the evening. If possible perform this Poojaa for 108 days to remove financial troubles Or you can recite Kuber Lakshmee Mool Mantra for 108 days. A photo of Goddess Lakshmee along with Sudarshan Kuber Yantra could be used for the Poojaa. The Mool Mantra is as follows :
"Kuber Twam Dhan desam Graha Te Kamal Stithaa
Tam Devem Prehayasu Twam Madgrahe te Namo Namah.

Akshaya Triteeyaa is also called Navaann Parv, Aakhaa Teej, or Akshaya Teej.

Akshaya Triteeyaa is traditionally observed as the birthday of Parushuraam also. Puraan speak about how he reclaimed the land from the sea. Goa and Konkan regions, even today, are referred to as Parashuraam Kshetra. At that time he settled 96 selected families there, called Shahanavkulee Braahman, who are said to have created the cultural heritage of this part of India.

New beginnings like weddings, business ventures, new deals, new audit books, business trips are considered to bring luck. Valuables bought on this day, such as gold is deemed auspicious. It is believed that gold multiplies if bought on this day. In Raajasthaan, this day is called Aakhaa Teej and is considered very auspicious for weddings as well.

The day gains more importance when it falls on a Monday or under Rohinee Star. A dip in the Ganges on this day is considered to be very auspicious. Out of the four - Dharm, Arth, Kaam and Moksh, Arth plays an important role in one's life. Arth means money. Even decades pass by, but the importance of Arth remains the same. Without Arth, nothing can be achieved. Here Arth merely does not only mean money but also includes honor, happiness etc. According to Shree Devee Bhaagvat Puraan, "A child can survive without his mother but he cannot survive without Lakshmee".

The Sun is a natural giver, giving freely to one and all. Those born in May are natural social reformers since they have an integral part of the Sun within them. They stand out brilliantly in life, easily overshadowing others.

Best Daan (charity) is to give a Brahmin in morning and can have following items :---
(1) Kalash filled with water.
(2) Hand Pankhaa (Fan)
(3) Chappal, slippers, Jootaa (not made of leather) in old times khadaaoon (made of wood) was given
(4) Chhaataa (umbrella)
(5) Gannaa (sugarcane)
(6) Sugar, Gud (jaggery), Dahee (yogurt), rice, milk, sweets of milk.
(6) Tarbooz (watermelon), Kharboozaa (melon)
(7) Laddoo.

It is said that by giving such Daan one enjoys Swarg, and many spiritual, material benefits. Cow feeding is also a Punya on this day, and feeding poor persons. It is said that if there is any astrological problem in match making, it can be solved to a great extent by marrying on this day.

Here is a list of Stotra, Mantra, and prayers to chant on Akshaya Triteeyaa.
Uda Kumbh Daan Sankalp (Mantra to chant at donating a pot) :
'Shree Parameshwar preetyaarth muda kumbh daanokt phal vaapyartham
braahman yoda Kumbh daanam karishye tadang kalash poojyaadhikam cha karishye'

Worship the pot and the Braahman with this Mantra and donate the pot to the Braahman
"Eesh dharm gato daataa brahmaa Vishnu shivaatmakah
Asya pradhaanatsa kalamaam santu manorathah"

Those who donate pot for the peace of their dead ancestors’ souls, they should Chant this Mantra:
"Pitroon makshaya triptyaarth mud kumbh daanam karishye" – Sankalp Mantra

Worship the Braahman and chant this Mantra while donating pot:
“Eesh dharm gato data brahmaa Vishnu shivaatmakah
Asya pradhaan triptyaantu pitarassa pitaamaha
Gandhodak tilairyuktam snaanam kumbh phalanvitam
Pitribhyassam pradaswaamee akshaya mupatishtathu”

Chandan Poojaa to Krishn on Akshaya Triteeyaa:
Worship Lord Krishn with Shodashopachaar and chant this Mantra while pasting Chandan to the idol.
“Yam karoti triteeya yaam,  Krishnam chandanam bhooshitam
Vaishaakh asyasite pakshe, Sayatyachyuta mandiram”

Parashuraam Jayantee Mantram :---
"Jamadagnya mahaaveer kshatriyaant kar prabho
Grahan arghyam mayadattam krupayaa parameshwaraa"
Chant this Mantra and offer Arghya to Parashuraam.

People try to cook whole food this day (without cutting them with knife in two or more pieces), for example, the whole small potato, the whole cluster beans, the whole small eggplants or brinjals, the whole leaves of Amaranth etc.