This
act of ritual cleansing is proven by the Quran, Sunnah (prophetic
tradition) and Ijmaa' (consensus of Muslim scholars). The Quran says
(what means):
"…And
if you are ill or on a journey or one of you comes from the place of
relieving himself or you have contacted women [i.e., had sexual
intercourse] and find no water, then seek clean earth and wipe over your
faces and your hands [with it]. Indeed, Allaah is ever Pardoning and
Forgiving." [Quran 4:43]
From the Sunnah, we have the Hadeeth (prophetic statement) related by Abu Umaamah 
in which the Prophet 
said: "All of the earth has been made a pure place of prayer for me and
my nation. Whenever a person from my nation wants to pray, he has
something with which to purify himself, that is, the earth." [Ahmad]
Finally,
there is a consensus that Tayammum forms a legitimate part of the
Sharee'ah (Islamic Law), as it replaces ablution with water or Ghusl
(ritual bathing), under specific circumstances.
A Blessing from Allah:
This form of ablution is viewed as a blessing from Allaah to the Muslims. Jaabir related that the Prophet
said: "I have been given five things that were not given to anyone
before me: I have been made victorious due to fear of a distance of one
month's journey; the earth has been made a place of prayer for me and a
source of purification - wherever and whenever any member of my nation
wants to pray, he may pray; and the war booty has been made lawful to
me, and this was not lawful to anyone before me. I have been given
permission to intercede. Prophets before me used to be sent to their own
people only, but I have been sent to all of mankind." [Al-Bukhaari
& Muslim]
When to Make Tayammum:
One is permitted to make Tayammum in any of the following cases:
1- If one cannot find water or the amount one finds is insufficient for ablution
'Imraan Ibn Husayn said: "We were with the Messenger of Allaah during a journey. When he led the people in prayer, one man stayed apart. He
asked him: "What prevented you from praying?" He replied: 'I need a
ritual bath (because of having a wet dream) and there is no water.' The
Messenger said: 'Use the soil, for it is sufficient (i.e. Tayammum).''' [Al-Bukhaari & Muslim]
2- If one is injured or ill:
If
one is in this condition and thinks that using water will worsen it (he
does not have to be absolutely sure, but may base his assumption on
past experience or what a knowledgeable person has told him), he may
perform Tayammum.
Jaabir
said, "We were on a journey and one of us was injured. Later, he had a
wet dream. He asked his companions, 'Can I perform Tayammum?' They
said, 'No, not if you have water.' He performed Ghusl, which caused him
to die. When news of this came to the Messenger of Allaah
he said: "They killed him! May Allaah kill them! Do you not ask if you
do not know? The remedy for ignorance is to ask. He could have
performed Tayammum and not dropped water on his wound, or wrapped it
with something, then wiped over the wrapping, and then washed the rest
of his body.""
3- If water is cold enough to physically harm the user:
Tayammum
is allowed when water is available but is too cold and cannot be
heated, or there is no public bathroom available. 'Amr Ibn Al-'Aas
narrated that he was once participating in a military expedition. He
had a wet dream during an extremely cold night, and was afraid that if
he performed Ghusl he would die. He prayed the morning (Fajr) prayer
with his companions. He then went to the Messenger of Allaah to ask him about this. The Messenger said: "O 'Amr! Did you pray with your companions while you needed a ritual bath?" 'Amr said to the Prophet the verse (which means): "…Do not kill yourselves [or one another]. Indeed, Allaah is to you ever Merciful." [Quran 4:29] The Prophet smiled at this and did not say anything. [Al-Bukhaari]
4- If water is nearby, but one cannot fetch it due to fear:
If
one fears for his life, family, wealth, [for example, if an enemy
(beast or human) is nearby or if one is a prisoner, and so on], he may
perform Tayammum. This is also allowed if there is water but one lacks
the proper means to get it, or if one fears some accusation against him
if he gets it.
5- If one is saving his water for later use:
This could be for dough, cooking, or to remove an impurity that is not pardonable. Imaam Ahmad 
said: "Many of the Companions performed Tayammum to save their water for drinking." 'Ali
said: "A man who is travelling and becomes unclean because of sexual
intercourse, or a wet dream, can perform Tayammum if he fears he will go
thirsty. He should perform Tayammum and not Ghusl." [Ad-Daaraqutni]
6- If one can get water, but fears that the prayer will be over by the time he gets it:
He can perform Tayammum and pray, and does not need to repeat his prayer (after he gets water).
The Soil Used for Tayammum:
It must be pure soil: this can be sand, stone, gypsum, and so on. Allaah Almighty Says in the Quran (what means): "…Perform Tayammum with pure soil..."
[Quran 5:6] and all scholars of the Arabic language agree that 'soil'
(in Arabic) is whatever covers the earth, dirt or otherwise.
How to Perform Tayammum :
First,
one must have the intention to perform ablution and purifying himself,
then he mentions Allaah's name, strikes the soil with his hands, and
wipes his face and hands up to the wrist, starting with the right hand.
Nothing is more authentic and clear than what 'Ammaar
related. He said: "I once became sexually impure and had no water, so I
rolled in the dirt and prayed. This was mentioned to the Prophet who said: "This
would have been enough for you," and he struck the earth with his
hands, blew in them and then wiped his face and hands with them." [Al-Bukhaari & Muslim]
This
Hadeeth shows that one strike of the earth is sufficient, and one only
wipes the arms to the wrists. It is an act of Sunnah that one who makes
Tayammum with dirt should blow into his hands first and not make his
face dusty or dirty.
What Tayammum Makes Permissible:
After
performing Tayammum, one is pure and may perform any of the acts
requiring prior ritual purification, such as praying and touching the
Quran. He does not have to perform it during the time of prayer, and he
may pray as many prayers as he wishes (unless he nullifies it), exactly
as it is the case with regular ablution. Abu Tharr reported that the Prophet
said: "The soil is a purifier for a Muslim, even if he does not find
water for ten years. Then, if he finds water, that is, to make ablution,
and so on, it becomes incumbent upon him to use it." [Ahmad &
At-Tirmithi]
In
Arabic, the word Tayammum literally means an 'aim' or 'purpose.' In
Islamic Law, it refers to: 'Aiming for or seeking soil to wipe one's
face and hands with the intention of purification and preparing oneself
to pray, and so on."