Some of the ritual practices of the Markandeya Purana are:

- The worship of Devi: The Devi Mahatmya is the most famous part of the Markandeya Purana, which narrates the glory of the Goddess and her victory over various demons. It consists of three episodes: the slaying of Madhu and Kaitabha by Vishnu's power as Yogamaya; the slaying of Mahishasura by Durga; and the slaying of Shumbha and Nishumbha by Kali and other forms of the Goddess. The Devi Mahatmya is a hymn of praise to the Goddess as the supreme power and creator of the universe. It also describes her various forms, names, attributes and manifestations. It is recited by devotees as a source of protection, blessing and liberation. The Devi Mahatmya is considered as one of the most important texts of Shaktism, and as a scripture of universal significance. The worship of Devi involves various rituals, such as chanting, offering, fasting, meditating, and celebrating festivals, such as Navratri, Durga Puja, and Kali Puja.

- The observance of yugas and kalpa: The Markandeya Purana is based on the concept of yugas, or cosmic cycles of time. According to the text, there are four yugas: Satya, Treta, Dvapara and Kali. Each yuga has a different duration, quality and morality. The Satya yuga is the golden age of truth, virtue and happiness, lasting for 1,728,000 human years. The Treta yuga is the silver age of sacrifice, ritual and kingship, lasting for 1,296,000 human years. The Dvapara yuga is the bronze age of war, heroism and decline, lasting for 864,000 human years. The Kali yuga is the iron age of strife, ignorance and suffering, lasting for 432,000 human years. The current age is the Kali yuga, which began in 3102 BCE according to the Hindu calendar. The Markandeya Purana describes the signs and symptoms of the Kali yuga in detail. It predicts that people will become greedy, dishonest, violent and immoral. They will lose respect for their elders, teachers and parents. They will neglect their duties and follow their passions. They will suffer from diseases, famines, wars and natural disasters. They will worship false gods and demons. They will forget the Vedas and the Dharma. They will become addicted to intoxicants and pleasures. They will have short lives and low intelligence. The Markandeya Purana also foretells the end of the Kali yuga and the dawn of a new Satya yuga. It prophesies that a great king named Kalki will appear at the end of the Kali yuga as an avatar of Vishnu. He will ride a white horse and wield a sword of fire. He will destroy the wicked and restore righteousness on earth. He will usher in a new era of peace and prosperity. He will revive the Vedas and the Dharma. He will rule for a thousand years as a universal monarch. The Markandeya Purana also contains a vision of the dissolution of the universe at the end of a kalpa, or a cycle of four yugas. It narrates how Markandeya witnessed the cosmic deluge while meditating on Shiva. He saw how Vishnu reclined on a serpent in the ocean of causation, holding all beings in his sleep. He saw how Brahma emerged from Vishnu's navel on a lotus and created the world again. He saw how Shiva danced on a dwarf and destroyed the world again. He saw how the cycle of creation and destruction repeated endlessly. He realized that the universe is an illusion and that only Shiva is the eternal reality. The observance of yugas and kalpa involves various rituals, such as performing sacrifices, following dharma, practicing yoga, and seeking liberation.

- The performance of samskaras: The Markandeya Purana also deals with various samskaras, or rites of passage, that mark the different stages of human life. The text describes the samskaras in detail, such as their significance, purpose, procedure, benefits and drawbacks. The samskaras include: garbhadhana (conception), pumsavana (fetus protection), simantonnayana (hair parting), jatakarma (birth), namakarana (naming), nishkramana (first outing), annaprashana (first feeding), chudakarana (hair cutting), karnavedha (ear piercing), vidyarambha (learning initiation), upanayana (sacred thread), samavartana (graduation), vivaha (marriage), vanaprastha (retirement), sannyasa (renunciation), and antyeshti (funeral). The performance of samskaras involves various rituals, such as chanting mantras, offering oblations, giving gifts, wearing symbols, observing vows, and honoring ancestors.

Source: 
(1) Markandeya Purana - Wikipedia. https://en.wikipedia.org/wiki/Markandeya_Purana
(2) A Brief Outline Of Markandeya Purana - GaneshaSpeaks. https://www.ganeshaspeaks.com/spirituality/hinduism/purana/markandeya-puran/
(3) Markandeya Purana – Vyasa Mahabharata. https://www.vyasaonline.com/markandeya-purana/