It's an important ministry of the church, praying for the sick. James mentions the prayer of faith for sickness as he concludes his letter. The word means "without strength, weak," expanding the circle to spiritual and emotional illness. There are crazies out there: send money for our anointed cloths and holy oil, miracle carrot seeds or whatever. Didn't get healed? Your fault, oh faithless one, says the fleecers. This writer cautions about two errors Christians fall for. Makes one want to run, not walk, away.
So what to do? Obey the Word. John Piper challenges elders to. Max Lucado has an instruction video (2:17) to encourage prayer for the sick. This British Baptist congregation explains the three needs listed in the passage. And this, a long article examining aspects of such prayers. Here's a woman's story, learning to pray for healing, because of her husband's multiple bouts of cancer. This differentiates between natural and supernatural healing (both are great) and sample prayers
We're used to extemporaneous prayers, but can benefit from written ones too. Here are 8 prayers from The Anglican Book of Common Prayer, most Scripture. Similarly, a passionate Quebecois group has prayers for the sick, again laced with prayer. This is a sampler of prayers, a little odd, with many dozens of comments showing the desperate condition of many needing prayer. Samples here and here, prayers for four types of sickness, including accidents, injuries, God's sovereignty.
Use oil? We use water for baptism, and bread/wine for the Lord's Supper. Yes, no magic, but tangible.