Who must be a witness to a conversion according to Jewish law?
The talmud quotes a baraisa from rabbi chiya bar abba in the name of rabbi yochanan that a convert must stand before three jewish men who form a beis din. (yevamos 46b) this is further recorded by maimonides in mishneh torah. (issurei biah 14:6)
Not all of those men have to be rabbis. the shulchan aruch states that three laymen can form a beis din, provided at least one of the men is knowledgeable in all the halacha. (choshen mishpat 3:1) The shach however maintains that it is a biblical obligation that all three of the men be knowledgeable. (ibid 3:1)
Nowadays it is almost universal that a convert stand before three trained rabbis.