The Torah instructs that the kohen use a עץ ארז as part of the purifying process of the metzora. This process is done immediately upon the recession of the nega.
Type of wood
The wood used is עץ ארז, known as the famed cedar of Lebanon wood. But, the story of rabbi Tarfon indicates that the used staff is crafted from the wood of the ברות variety of cedar known as the juniperus excelsa.
Chazal mention that there are 24 types of ארז, one of them called ברוש which is translated by the Talmud (בבא בתרא פ עמוד ב) as ברתי -some understand the closeness of ברתי to the term ברות Rabbi Yehudah mentioned as the material Rabbi Tarfon’s purifying staff was made of.
The length of the staff is one amah while its circumference is that of the כרע המטה -the leg of a bed.
The כרע המטה measurement gets tricky as no chazal sources specify just how thick their bed legs where.
However, a hint can be derived from the Talmudic discussion of placing an egg under the bed-legs (ביצה ג עמוד ב), so placing the circumference of the egg as the same as the bed leg is the closest we can get to determining the desired thickness of the staff to be used.
The tip of the staff
Rabbi chaninah Ben gamliel says that the tip of the staff should have a טרף to it. Some describe this teref as leafy, while some describe it as groovy, both descriptions citing the reason for it so that it can hold/absorb the spring water that is sprayed during the Taharah process.