This puja is mentioned in the Ishanashivagurudeva Paddhati, and is a festival celebrating the spring season along with Damanakotsava , the associated festival of love, dedicated to Kama. In this puja, the season of spring is treated and worshipped as a goddess.
In case anyone is not aware, Vasanta, the god of spring and flowers, is the best friend of Kama (and Rati). He was mentioned to have been born from the sigh of Brahma in the Kalika and Shiva Puranas.
Vasantaradhana is one of the favorites of Shiva. The important part of worship in this festival held during the spring season (Vasantartu) is the Damanaka Puja, wherein Damanaka is an aromatic plant, and special to Kama since it was this plant that turned out to be the object of his Sapamoksha. Siva also blessed Kama, saying that whoever worships him with the Damanaka plant along with Vishnu, Brahma and other Devas will have all their wishes fulfilled. The author further states that those who do not strictly adhere to the Saivite modes of worship as stated above are, in effect, rejecting the basic tenets of Saivagama (traditionally communicated wisdom).
How The Puja Is Carried Out
For the details related to Vasantapuja and Damanakotsava, the author of the Paddhati has relied on 'Svacchandatantra' (official book of Kashmiri Shaivism) and 'SomaSambhupaddhathi' (another manual for Shaivite rituals).
The venue for Vasantapuja has to be a garden that abounds in Damanaka creepers and Asokavrkshas (Ashoka trees). Puja is begun with the invocation and Aradhana of Ganesh in Nirti angle and Guru in Isana.
It is under the shade of an Asokavrksha that Puja takes place. Two pots of sanctified water are placed at the foot of the Asokavrksha. The one on the right side is meant for Vasanta and that on the left for Kama. The presence of their consorts, Kusumavati and Padmavati respectively, have also to be kept in mind. In the middle of the Pujavedi, the Asokavrksha is conceived as Vasanta in the guise of a vibrant youth, golden in complexion, and is to be invoked and offered Gandha-puspa-nivedyantapuja. The nine powers of Vasantartu are Ahladini, Gandhavati, Surabhi, Malini, Madira, Madayanti, Rama, Pushpavati and Vasanti.
Next is the worship of the Damanaka plant, during which the Bhairava form of Siva has to be conceived in mind. Kama has also to be conceived as remaining seated along with his consort Rati on his right thigh and holding Puspasara in his right hand. He is served on all sides by a group of beautiful and shapely maidens. The Saktidevatas of Kama may also be conceived and offered Gandhadhupa-nivedyantapujas. The Gayatrimantra of Kama is also given.
The important feature of the festival on the second day is the collection of the Damanaka plant (the whole plant including the roots) from the garden in a pot, offering of Puja, followed by the ceremonial procession carrying the three pots (Damanaka, Kama and Vasanta) on an elephant in Nagarapradaksina, to the accompaniment of Nrtta-vadyasangita-ghoshas. On conclusion of the procession, the pots are placed beside the idol of Shiva after which Homavidhis, Sampatasparsa, Bali, prayer and Archana are performed. The other customary acts like Dakshina and gifts to the priests are also recommended. The Patala concludes with the following observation by the author.
ittham vasantavihitam savasantayagam proktam tadantamiha damanakam hi parva| yadvad vasantatilakam sumanobhiramam tadvanmaunobhisitan phalatiha kaman |
Though this festival is no longer celebrated in Kerala, another festival called Vasanta Panchami, also known as Sri Panchami, is observed religiously, mainly as Saraswati Puja and also as worship of Kama, Rati, Indra, Varuna and Brahma, on a grand scale, especially in Bengal, Punjab and most of North India. The legend also bears close resemblance to that of 'Vasantotsava' described in Isanasivagurudeva-paddhati. Legend has it that on this day Shiva turned Kama into ashes.
Source: Study of Ishanashivagurudeva Paddhati by J.P. Prajith (2008)
I have taken most of the excerpts word-for-word from there.