You might start by saying that although the ancient Christian practice of venerating the relics of saints, especially martyrs, can be abused in a superstitious way by some who misunderstand the purpose of relics, it is not itself in any way superstitious.
A relic is an object, such as a piece of clothing or, more commonly, a piece of bone from a saint's body, which has spiritual value because it belonged to one of God's saints. The Bible records many accounts of the value of relics and even episodes of miraculous events connected with them. "People brought to [Jesus] all who were sick and begged him that they might only touch the tassel on his cloak, and as many as touched it were healed" (Mt 14:35-36; cf. Mk 6:56; Lk 8:43-44). It was not uncommon for ordinary objects, like the tassel on the Lord's cloak, to have miraculous characteristics. Look also at Acts 5:15, where even Peter's shadow could cause miraculous healings.
Regarding the relics of saints, especially martyrs (about whom the Bible says, "Precious in the eyes of the Lord is the death of his holy ones" [Ps 116:15]), look at 2 Kings 13:21:
Elisha died and was buried. At the time, bands of Moabites used to raid the land each year. Once some people were burying a man, when suddenly they spied such a raiding band. So they cast the dead man into the grave of Elisha and everyone went off. But when the man came in contact with the bones of Elisha, he came back to life and rose to his feet.