Tayammum (Dry ablution)

Definition
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."
Proof of its Legitimacy
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 Allaah
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.""