Fiqh-us-Sunnah Volume 1, Purification and Prayer, Fiqh 1.066B.

First, one must have the intention (see the section on ablution). Then, he mentions Allah’s name, strikes the soil with his hands, wipes his face and his hands up to the wrist. Nothing is more authentic and clear than what ‘Ammar related. He said, “We became sexually impure and had no water, so we rolled in the dirt and prayed. This was mentioned to the Prophet and he 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.” (Related by al-Bukhari and Muslim). In another text he states, “It would have been enough for you to strike the ground with your hands, blow into them, then wipe your face and hands up to the elbows.” (Related by ad-Daraqutni.)

This hadith shows that one strike of the earth is sufficient, and one only wipes the arms to the wrists. It is from the sunnah that one who makes tayammum with dirt should blow into his hands first and not make his face dusty or dirty.