Tayammum

Tayammum is an act of worship consisting of wiping the forehead and the two hands. It is a substitute for wudu' and ghusl.
Tayammum is performed in place of Wudhu or Ghusl when:

1.      Not enough water is available for Wudhu or Ghusl.

2.      Obtaining water for Wudhu will endanger your life or property or you are unable to procure water by any means.

3.      Using the available water will leave insufficient water for drinking and pose a risk of dying of thirst or illness, or difficulty for yourself or your dependents.

4.      Washing your face and hands with water will endanger your health.

5.      Water is available but you do not have permission to use it.

6.      There is a risk that performing Wudhu or Ghusl will cause the time of the entire or a part of the prayer to end.

7.      If the body or clothing is ritually impure (najis) and the person possesses only as much water so that if he was to perform Wudhu or Ghusl, no more water would be available for making his body or clothing pure for prayer.

MANNER OF PERFORMING TAYAMMUM

Niyya:

Make your intention as, "I am doingTayammum in place ofWudhu (orGhusl), for the pleasure of Allah and to seek closeness to Him."

Step 1:

Strike the palms of hands simultaneously on earth, sand, or stone (in order of preference) which is dry and clean.

Step 2:

Pull both palms together from the beginning of the forehead where the hair grows down to the bridge of the nose.  Both sides of the forehead joining the ears and over the eyebrows should be included.

Step 3

:Then pull the left palm on the whole back of the right hand from the wrist bone to the fingertips.

Step 4

:Then pull the right palm on the whole back of the left hand.
Step 5: Strike the palms together upon a valid surface a second time as in Step 1.Step 6: Repeat Step 3.

Step 7:

Repeat Step 4.
This manner of Tayammum is based on the ahadith which have elaborated on the words of the Qur'an which say, "Do Tayammum...by wiping a part of your face and your hands."

Taken from: al-islam.org