What is the correct way to perform tayammum (dry ablution)? And has a sound hadith been narrated proving the wiping of the hands up to the elbows in it?

The Hanafis and Shafi'is held that tayammum (definition) involves two strikes, while the Malikis and Hanbalis maintained it is a single strike. The correct view is that tayammum is a single strike for the face and palms only. This is supported by the authentic hadiths reported from the Prophet, peace and blessings be upon him. Al-Bukhari narrated from Ammar ibn Yasir that the Prophet, peace and blessings be upon him, said to him: "It suffices you [to wipe] your face and your palms." Furthermore, it is established from his action, peace and blessings be upon him, that he struck the ground with his hand a single strike, then wiped his face and palms with it.