Tayammum

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that he said: "When the verse of tayammum (dry ablution) was revealed, I did not understand how I should perform (tayammum), so I came to the Prophet (peace and blessings be upon him) to ask him about it, but he (peace and blessings be upon him) was not there. Then I went out searching for him and met him (peace and blessings be upon him). When he (peace and blessings be upon him) saw me, he (peace and blessings be upon him) understood the purpose for which I had come, so he (peace and blessings be upon him) struck both his hands on the ground and then wiped his face."
This narration is munqati' (has a broken chain).

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that some people came to the Messenger of Allah (peace and blessings be upon him) and said: "We are people who live in a sandy (desert) region, and we become junub (in need of ghusl), and among us are women in menstruation and postnatal bleeding, while we do not find water for four months at a time (so what should we do in such a situation)?" At this the Prophet (peace and blessings be upon him) said: "Hold to the earth (that is, perform tayammum)."
There is weakness in its chain.

It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that "the Prophet (peace and blessings be upon him) was on a journey, and when the time of prayer came, all the people dismounted from their mounts. A shepherd saw them, so he too came down (from a hill or height), struck his hand on the clean earth and performed tayammum, and then gave the call to prayer (adhan)."
There is weakness in the chain of this hadith.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that he said: I saw the Prophet (peace and blessings be upon him) pass water after relieving himself (that is, he urinated), and then he (peace and blessings be upon him) wiped with earth (performed tayammum). So I said to him (peace and blessings be upon him): (O Messenger of Allah!) Water is available very close to you! The Prophet (peace and blessings be upon him) said: "What do I know? Perhaps I may not reach it (the water) (and the time of my death may come before that)."
This narration is da'if (weak).

It is narrated from Sayyiduna Ali (may Allah be pleased with him) that he said: "Tayammum must be performed (anew) at the time of every prayer."
This narration is da'if (weak).

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that he said: "The finest and best soil on the face of the earth is that which has been ploughed for cultivation (that is, farm soil)."
This narration is mawquf (a Companion's statement) and hasan (good).