Tayammam is a way of purifying oneself with clean sand if there is no water available.
Clean earth is sufficient for a Muslim as a substitute for water for ablution (if he does not find water)
Narrated `Aisha:
(the wife of the Prophet) We set out with Allah’s Messenger (ﷺ) on one of his journeys till we reached Al- Baida’ or Dhatul-Jaish, a necklace of mine was broken (and lost). Allah’s Messenger (ﷺ) stayed there to search for it, and so did the people along with him. There was no water at that place, so the people went to Abu- Bakr As-Siddiq and said, “Don’t you see what `Aisha has done? She has made Allah’s Apostle and the people stay where there is no water and they have no water with them.” Abu Bakr came while Allah’s Messenger (ﷺ) was sleeping with his head on my thigh, He said, to me: “You have detained Allah’s Messenger (ﷺ) and the people where there is no water and they have no water with them. So he admonished me and said what Allah wished him to say and hit me on my flank with his hand. Nothing prevented me from moving (because of pain) but the position of Allah’s Messenger (ﷺ) on my thigh. Allah’s Messenger (ﷺ) got up when dawn broke and there was no water. So Allah revealed the Divine Verses of Tayammum. So they all performed Tayammum. Usaid bin Hudair said, “O the family of Abu Bakr! This is not the first blessing of yours.” Then the camel on which I was riding was caused to move from its place and the necklace was found beneath it. (Sahih Bukhari)
Narrated Jabir bin `Abdullah:
The Prophet (ﷺ) said, “I have been given five things which were not given to any one else before me. -1. Allah made me victorious by awe, (by His frightening my enemies) for a distance of one month’s journey. -2. The earth has been made for me (and for my followers) a place for praying and a thing to perform Tayammum, therefore anyone of my followers can pray wherever the time of a prayer is due. -3. The booty has been made Halal (lawful) for me yet it was not lawful for anyone else before me. -4. I have been given the right of intercession (on the Day of Resurrection). -5. Every Prophet used to be sent to his nation only but I have been sent to all mankind. (Sahih Bukhari)
The performance of Tayammum by a non-traveller (is permissible) when water is not available and when one is afraid that the time of Salat (prayer) may elapse
How to perfom Tayammun
Narrated `Abdur Rahman bin Abza:
`Ammar said to `Umar “I rolled myself in the dust and came to the Prophet (ﷺ) who said, ‘Passing dusted hands over the face and the backs of the hands is sufficient for you.’ ” (Sahih Bukhari)
Place your hands on clean earth on the floor/ tyles
Blow off the dust on your hands
wipe your face
wipe your right arm to the elbow
wipe your left arm to the elbow
Narrated `Ammar:
The Prophet (ﷺ) stroked the earth with his hands and then passed them over his face and the backs of his hands (while demonstrating Tayammum). (Sahih Bukhari)