The story of Tulasi Vivaha is as follows:
According to Devi Bhagavatam, Brinda wanted to marry Lord Vishnu and performed penance for the same. Lord Vishnu appeared before her and said that He could not marry her in this birth. He told her to marry someone else for this birth and He would be her husband in the next birth. She met and fell in love to marry the Asura Shankhachuda. According to Devi Bhagavatam, this asura had a part of Lord Krishna in him. According to Padma Purana, the name of the Asura was Jalandhar.
The Asura was a devout Shivite and was very powerful. His power also increased after his marriage to Brinda, due to her pativratya. No one was able to defeat him. Some people say all the Devas went to Lord Vishnu to solve the problem. Some others say that it is Lord Krishna that they approached. Lord Vishnu (or Lord Krishna) told them that the Asura is powerful because of her strong chastity. If her chastity was destroyed, the Asura could also be destroyed.
Lord Vishnu approached Brinda in the guise of Shankhachuda and asks for intimacy at an odd time. Some people said that Lord Vishnu destroyed her chastity because she complied thinking it was her husband. Some people say that Brinda realized that it is not her husband. She cursed Him that He became very dark and became a stone. Lord Vishnu reminded her that she had desired Him as her husband and He had given her the boon that He would marry her in her next birth.
Some say that she cursed Lord Vishnu after her chastity was lost. Some say that she cursed before Lord Vishnu could do anything and jumped into a river to give up her life. Some people say that the Asura could be vanquished because she had lost her chastity. Some say that she drowned and so he could be vanquished, in her absence. Brinda was reborn as Tulasi Plant and Lord Vishnu became a fossil in the River Gandaki. The fossil is now called Shalagrama, which is seen in several forms of Lord Vishnu and can be identified by experts.
Thus, we perform the wedding of Tulasi Plant with Shalagrama. Some people even say that Goddess Lakshmi turned into Tulasi Plant after killing some asuras. That is why we celebrate the wedding of Goddess Lakshmi with Lord Vishnu as well. And since Adi Shankaracharyar created a rain of gold coins with the help of an amla fruit, amla is considered as a part of Goddess Lakshmi. Thus, we also place an amla fruit with Shalagrama. We are sharing the photograph celebrations at our home as well.