To perform Mangala Gowri Vratham, follow these steps:

1. Cleanse yourself and the puja area. Dress in traditional attire and gather the necessary puja items like turmeric, vermilion, flowers, fruits, betel leaves, betel nuts, camphor, incense, and a lamp.
2. Place a picture or idol of Goddess Gowri on a decorated puja platform. Light the lamp and offer prayers to Lord Ganesha, seeking his blessings for the successful completion of the Vratham.
3. Recite the Mangala Gowri Vratham Katha or story, which highlights the significance of the Vratham and the virtues of Goddess Gowri.
4. Offer flowers, turmeric, vermilion, and other traditional items to the Goddess. Perform aarati by moving the lit lamp in a circular motion in front of the deity.
5. Offer fruits, betel leaves, and nuts as naivedyam (offering). Pray to the Goddess for marital harmony, well-being, and prosperity.
6. Conclude the Vratham by seeking forgiveness for any mistakes committed during the puja. Distribute prasad among family members and seek their blessings.
7. On subsequent Tuesdays, you can continue to perform the Vratham with devotion and faith, following the same procedure.

It is advisable to consult with a knowledgeable person or a priest for any specific rituals or variations based on personal beliefs or traditions.