General Ruling Source: https://islamqa.info/en/answers/21074/description-of-tayammum
Scroll down further for hanafi fiqh specific ruling.
Al-Bukhaari and Muslim narrated the hadeeth of ‘Ammaar ibn Yaasir describing tayammum. Al-Bukhaari narrated it in a number of places in his Saheeh. One of these reports (no. 347; 1/455 of Fath al-Baari) says: “ ‘It would have been sufficient for you to do this’ – then he struck the palms of his hands on the ground, then dusted them off, then wiped the back of each hand with the other, then he wiped his face with his hands.”
Abu Dawood (317; 1/515 of ‘Awn al-Ma’bood) narrated it with the same isnaad as al-Bukhaari, apart from the shaykh of al-Bukhaari (Muhammad ibn Salaam), instead of whom he mentioned Muhammad ibn Sulaymaan al-Anbaari, of whom al-Haafiz said in al-Taqreeb (2/167): he is sadooq (truthful). This version of the report says: “He struck his hands on the ground and dusted them off, then he struck his right hand with his left hand, and his left hand with his right hand, then he wiped his face.”
Al-Haafiz mentioned in al-Fath (1/457) that al-Ismaa’ee’li narrated it with the wording: “It would have been sufficient for you to strike your hands on the ground, then dust them off, then wipe your right hand over your left and your left hand over your right, then wipe your face.”
Al-Shanqeeti said in Adwa’ al-Bayaan (2/43): “This hadeeth of al-Bukhaari states that the hands should be wiped before the face.”
Shaykh al-Islam said in al-Fataawa (21/423): “The report of al-Bukhaari clearly shows that the back of the hand should be wiped before the face. The fact that in another report he said ‘the back of the hand’ indicates that he wiped the back of each with the palm of the other.” He also said (21/425: “But the report which was narrated only by al-Bukhaari shows that he wiped the backs of the hands before the face.”
(See al-Fataawa, 21/422-427)
Based on this, the way in which tayammum is done is to say Bismillaah with the intention of doing tayammum, then strike the ground once with the palms of the hands, then wipe the back of the right hand with the palm of the left, and the back of the left hand with the palm of the right, then wipe the face with both hands. Then the same du’aa’s that are recited after wudoo’ should be recited after tayammum. And Allaah knows best.
The following answer is based on Hanafi Fiqh Source: https://seekersguidance.org/answers/hanafi-fiqh/how-to-make-dry-ablution-tayammum/
How to Perform Tayammum
 Intend to lift the state of ritual impurity,
 say the basmala,
 strike the earth [or anything of the top surface of the earth like a stone],
 wipe your face entirely,
 strike the earth [or its equivalent] a second time,
 wipe the right arm completely up to and including the elbow, and then the left arm likewise.