In East Asian Mahayana Tradition, they do contemplative recitation & bowing prostrations using His Name, recite His Mantra and Sutras and plus in the Chinese Mahayana, there is a sadhana which some have told me it's Tian Tai in origin, is a three part repentance ritual based on the Medicine Buddha Sutra texts known as 'The Compassionate Medicine Master Jeweled Repentance' which is recited annually during the prescribed liturgical celebration or like one organisation I know which does it once a month or any time of the year as deem fit, which can be done in one day or stretched to three days. So far, I have encountered two versions of this sadhana practice, one version here
In the Chinese Mahayana Tradition, generally, the Medicine Buddha is the next most popular after Amitabha Buddha. In many Chinese Buddhist temples / monasteries / centres, they usually have the famous triad of Sakyamuni Buddha in the center, Amitabha Buddha on the right and Bhaisajyaguru on the left. I have read from some scholastic writings that formerly in ancient times, Akshobhya Buddha was popular but somehow eclipsed by Bhaisajyaguru later on perhaps due to myriad forces like political & social patronage rather than purely doctrinal issues.
In the East Asian Mahayana Trads that follow the Chinese liturgical & lunar calendar (with exception of Japan), He is commemorated on the last day of the 9th Lunar Month, depending on the year calculation which has the 29th or 30th day for that month. In bigger Chinese Mahayana temples / monasteries, they have a side shrine to the Medicine Buddha known as the 'Eastern Hall of Merits', normally on the left side of the main shrine hall and chants are offered at every New & Full Moon Upavasatha Days and special liturgical celebrations during the year and in the daily offerings.
His devotion is popularly practiced for mundane reasons like healing, overcoming / pacifying obstacles, longevity, for liberation of lower realms sentient beings as well and the supramundane ones as seeking birth in His Eastern Pure Lapis Lazuli Land for attainment and accomplishment of the Bodhisattva Path for Supreme Buddhahood for all parent sentient beings. So, they will have red paper dedication plaques for the above mentioned purposes on the altar in front and at the sides of the Bhaisajyaguru Buddha image, lighting of numerous lamps with the standard 49 lamps (as per the Sutra) and up until 108, hanging of various banners and streamers with the auspicious name or image of Bhaisajyaguru Buddha and His Bodhisattvas decorating the shrine hall, observing the vegetarian 8 Precepts for 7 days and nights as per the Sutra and other numerous offering activities.
Typically, in traditional East Asian Mahayana iconography:
a. The Medicine Master Lapis Lazuli Radiance Tathagata would be depicted in Bhikshu robes, golden hue body (some modern renditions would depict him in lapis lazuli color), seated on a lotus throne, right hand holding a medicinal plant twig (varies with artforms, some depicting a rebirth mudra), left hand or both hands on each other upturned holding a stupa / pagoda or medicine bowl
b. The Buddha entourage: of the 'Eight Medicine Buddhas Brethren' either above or on the Medicine Master Lapis Lazuli Radiance Tathagata's left / right sides
(6 Tathagatas: King of Clear Knowing, Melodious Ocean of Dharma, Supreme Glory Free From Sorrow, Stainless Excellent Gold, King of Melodious Sound & Glorious Renown of Excellent Sign, Sakyamuni Tathagata: as the Host Buddha of the current Dispensation in our Saha World and the main Host Buddha of the Eastern Pure Lapis Lazuli Land, the Medicine Master Lapis Lazuli Radiance Tathagata)
c. The Bodhisattva entourage:
Eight Great Bodhisattvas: 2 Host Bodhisattvas of the Pure Lapis Lazuli Land: the Moon Radiance Bodhisattva on His Right (depicted as carrying a crescent moon or a Sutra text), the Sun Radiance Bodhisattva (depicted as carrying a sun or a medicine bowl), 6 other Bodhisattvas as per Sutra text: Manjusri Bodhisattva, Avalokitesvara Bodhisattva, Mahastamaprapta Bodhisattva, Inexhaustible Intention Bodhisattva, Jewelled Udumbara Flower Bodhisattva, Medicine King Bodhisattva, Medicine Superior Bodhisattva and Maitreya Bodhisattva.
d. The Dharma Protectors entourage:
The 4 Great Heavenly Kings: Vaisravana, Virudhaka, Dhrtrarastra & Virupaksa.
The 12 Great Yaksa Generals: General Kimbhiro, General Vajra, General Mekhilo, General Antilo, General Anilo, General Santhilo, General Indalo, General Payilo, General Mahalo, General Cidalo, General Caundhulo, and General Vikalo.
Connection with the Amitabha Buddha & Sukhavati
The merit, virtue, and adornments of this Land are identical to those of the Western Land of Ultimate Bliss."
Moreover, Manjushri, there may be those among the fourfold assembly of Bhikshus, Bhikshunis, Upasakas and Upasikas, as well as other good men and women of pure faith, who accept and uphold the eight precepts either for one year or for three months, practicing and studying them.
With these good roots, they may vow to be born in the Western Land of Ultimate Bliss where the Buddha of Limitless Life dwells, to hear the Proper Dharma, but their resolve may not be firm.
However, if they hear the name of the World Honored One, Medicine Master Vaidurya Light Tathagata, then as the end of their lives draws near, before them will appear Eight Great Bodhisattvas, whose names are: Manjushri Bodhisattva, The Bodhisattva Who Observes the Sounds of the World, Great Strength Bodhisattva, Inexhaustible Intention Bodhisattva, Jeweled Udumbara Flower Bodhisattva, Medicine King Bodhisattva, Medicine Superior Bodhisattva, and Maitreya Bodhisattva.
Those Eight Great Bodhisattvas will appear in space to show them the way, and they will naturally be born by transformation in that Land, amid precious flowers of a myriad colors.