On Paush Purnima and Makar Sankranti, devotees take bath in holy rivers like Ganga, Yamuna, Narmada, Shipra. If it is not possible to take bath in the river, then you can take bath at home by mixing Ganga water in water. It is said in the Puranas that taking a river bath on Paush Purnima destroys sins and fulfills wishes. The bathing of Magh month also starts from this day.
After bathing in the river, one should donate food, clothes, sesame and jaggery to the needy people on the river bank or around their house or around any temple. It is said in the scriptures that donations made on this full moon day yield hundred times more virtuous results than on normal days.
Sun must be worshiped on the full moon day of Paush month, because there is a tradition of worshiping the sun throughout this month. Offer Arghya to the Sun on the last date of Paush month. For this, use a copper pot and offer water to the Sun while saying Om Suryay Namah. It is written in Vishnu Purana and Brahmavaivartapurana that worshiping the Sun brings happiness, peace and success to the devotee.
Recite the scriptures as per your time on Paush Purnima. Chant mantras. You can listen to the story of some saint.
Special anointment of Lord Shiva should be done on the full moon day. Offer water, milk and Panchamrit to Shivalinga.
After moonrise on the evening of full moon, Arghya should be offered to Moon God with milk and water. Use silver or clay urn for this. While offering Arghya, chant the mantra Om Son Somay Namah.
There is also a tradition of taking bath by mixing sesame seeds in water on this full moon day. On this day, offer jaggery and sesame seeds to God. After puja, consume sesame seeds and jaggery and donate it.
There is a tradition of serving cows on this day. Take care of cows in a cowshed. Feed green grass to cows. Donate money to the cow shelter.