It does say that you need two or three witnesses (with or without sin) and that the witnesses themselves must throw the first stones.
At the mouth of two witnesses, or three witnesses, shall he that is worthy of death be put to death ... The hands of the witnesses shall be first upon him to put him to death. Deuteronomy 17:6And if you're stoning your wife, family member, or friend for believing in the wrong god, then you must throw the first stone (and you may not pity her).
If thy brother, the son of thy mother, or thy son, or thy daughter, or the wife of thy bosom, or thy friend, which is as thine own soul, entice thee secretly, saying, Let us go and serve other gods ... Thou shalt not consent unto him, nor hearken unto him; neither shall thine eye pity him, neither shalt thou spare, neither shalt thou conceal him: But thou shalt surely kill him; thine hand shall be first upon him to put him to death. Deuteronomy 13:6-9
But who can participate in the stoning? Is stoning just for men, or can women and children throw some stones too?
Well, as usual, the Bible isn't much use here. Sometimes it says just the men (Deuteronomy 13:9, 22:21) should do the stoning, and sometimes all the people get to do it (Leviticus 24:23, Numbers 15:32, 17:7, 21:21, Joshua 7:25).
But luckily Monty Python clears the whole thing up in the Life of Brian.
Monty Python - The Life Of Brian (The Stoning)