Question: Where does the Torah speak about washing the hands?
Answer: Washing the hands and feet is referred to many times in the Bible. There was a washing basin in the Tabernacle where the priests washed their hands and feet before entering (Ex.30:18-21). Washing the hands is specifically mentioned in Deut.21:6 (see also Lev. 15:11) and in Psalms 26:6 and 73:13.
An entire tractate of the Mishnah (Yadayim) is devoted to impurity of the hands. Washing the hands before eating is discussed in the Mishnah in (for example) Berachos Ch.8. The laws about washing the hands on arising are codified in Shulchan Aruch Orach Chayim Sec.4; the laws about washing the hands before eating, in Sec.158ff.
Yours, Rabbi Azriel Schreiber