his pbuh authentic narrations state that he pbuh wiped over his leather footwear while at home and travelling. he specified a limit of one day and night for residents to wipe over them, and three days and nights for travellers.
he pbuh used to wipe over the upper part of the shoes or stockings. (he also wiped over the turban alone or along with the forehead.)
he pbuh acted according to the condition of his feet: if he was wearing shoes or stockings he wiped over them, and if his feet were bare he washed them.h performed tayammum from the type of ground on which he was praying, be it dust, soil or sand, and said: "wherever someone of my ummah may be when prayer is due, he has his mosque and his source of purification."1
he pbuh neither carried sand with him on long journeys nor did he order his companions to do so.
no authentic narration showed that he pbuh did tayammum for every prayer or ordered that it be done. he simply considered tayammum as a substitute for ablution.
he pbuh used to perform tayammum by striking the ground once for wiping over both the face and hands.2
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1 narrated by ahmad.
2 tayammum is limited to the face and hands and does not include the parts of the body washed in wudhu'.