Lord Skanda is son of God Shiva and Goddess Parvati also known as Murugan, Kartikeyan and Subramanya. The Shasti tithi coming after Amavasya (new moon night) is the one meant for fasting.
Devotees listen to stories related to Skanda and reading of Skanda Purana. Another activity during the day is the reciting of Kanta Shasti Kavasam.
Fasting is not just abstaining from food but it also an attempt to instill positive thoughts. Many people use fasting as a means to fight against anger, lust, impatience and other negative tendencies.