I took several holy cards to view and touch relics of the saints. Now do I keep the relic and pray for someone or give it to the person so that he/she can pray for healing?
How can a relic help a sick person?
From the tone of body of your question, I am presuming that you would like a Catholic response. That is the perspective I am going to give for you.
Holy Cards touched to the relics of the saint are third class relics.
The Catholic church divides relics into three classes:
First-Class Relics: items directly associated with the events of Christ's life (manger, cross, etc.) or the physical remains of a saint (a bone, a hair, skull, a limb, etc.). Traditionally, a martyr's relics are often more prized than the relics of other saints. Parts of the saint that were significant to that saint's life are more prized relics. For instance, King St. Stephen of Hungary's right forearm is especially important because of his status as a ruler. A famous theologian's head may be his most important relic. (The head of St. Thomas Aquinas was removed by the monks at the Cistercian abbey at Fossanova where he died.) If a saint did a lot of traveling, then the bones of his feet may be prized. Catholic teaching prohibits relics to be divided up into small, unrecognizable parts if they are to be used in liturgy (i.e., as in an altar; see the rubrics listed in Rite of Dedication of a Church and an Altar).
Second-Class Relics: items that the saint owned or frequently used, for example, a crucifix, rosary, book, etc. Again, an item more important in the saint's life is thus a more important relic. Sometimes a second-class relic is a part of an item that the saint wore (a shirt, a glove, etc.) and is known as ex indumentis ("from the clothing").
Third-Class Relics: any object that is touched to a first- or second-class relic. Most third-class relics are small pieces of cloth, though in the first millennium oil was popular; the Monza ampullae contained oil collected from lamps burning before the major sites of Christ's life, and some reliquaries had holes for oil to be poured in and out again. Many people call the cloth touched to the bones of saints "ex brandea". But ex brandea strictly refers to pieces of clothing that were touched to the body or tombs of the apostles. It is a term that is used only for such; it is not a synonym for a third-class relic.
Many holy cards have a prayer on the back of them invoking the particular saint who's image appears on the front of the holy card. You are quite free to pray this prayer for the intentions for yourself or for the healing (or some other grace) of another person. You are also free to give to someone. If the person you are giving the holy card to is not really into praying, yet freely accepts the holy card from you, it is quite fine that you can do the praying for them. Prayer is never in vain. You could also place the holy card, while praying for a healing on the place of one's suffering. I would suggest that you perhaps try praying a novena to the saint in question at the same time.
I cannot find the story on the internet, but several years ago I was reading life in French of the Little Flower, St. Therese of Lisieux and how she had offered her last Holy Communion, on August 19, 1897, for Fr. Hyacinthe Loyson who had left the priesthood and eventually got married. Some years later an exorcist placed the holy card with the image of St. Therese of the Little Flower on the head of the possessed and and demon admitted to the particular priest, Fr. Hyacinthe had converted and repented of his sins on his death bed and was saved though the intercession of St. Therese of Lisieux. (If anyone knows of a link about this story please place it in here). As you see holy cards and holy images are to be treasured.
Matthew 9:20-22 (DRB) And behold a woman who was troubled with an issue of blood twelve years, came behind him, and touched the hem of his garment. 21 For she said within herself: If I shall touch only his garment, I shall be healed. 22 But Jesus turning and seeing her, said: Be of good heart, daughter, thy faith hath made thee whole. And the woman was made whole from that hour.
It is our disposition to have faith in God's healing power that heals us, not the relic itself as such (by which I mean that they are to no effect for one without faith; or at least opposed to faith). Although God may confer upon an object healing power extrinsically (e.g. Acts 19:11-12), these are only aids to faith, or tokens to help us place saving—or healing—faith in Him. That is to say, miracles leading on to the faith which saves: to believe God is with Paul is to accept the gospel he tireless preaches as truth, and so be saved by believing it salvifically.
This does not mean relics are no more special than any other object, they are 'most dear to God for the sake of' their original beareres (i.e. saints qua those who bore witness to the truth and show forth the glory of God), we might say; and that is perhaps the only reason 'they' have healing power. Do we think that Jesus' clothing had healing in its physical makeup anywhere? On the other hand, do we think that God the Father would not punish someone who would seek to defile or otherwise disrespect this possession of Jesus, which clothed Him—the very Temple of God—and reward those who, contrariwise, honor and venerate it as such (and not beyond)?
It then stands to reason that the one with more faith is more likely to benefit from this sacramental.