One of the best summaries on this topic came from Brigham Young: 
 
"If we are sick, and ask the Lord to heal us, and to do all for us that is necessary to be done, according to my understanding of the Gospel of salvation, I might as well ask the Lord to cause my wheat and corn to grow, without my plowing the ground and casting in the seed. It appears consistent to me to apply every remedy that comes within the range of my knowledge, and to ask my Father in Heaven, in the name of Jesus Christ, to sanctify that application to the healing of my body. 
 
"But suppose we were traveling in the mountains, … and one or two were taken sick, without anything in the world in the shape of healing medicine within our reach, what should we do? According to my faith, ask the Lord Almighty to … heal the sick. This is our privilege, when so situated that we cannot get anything to help ourselves. Then the Lord and his servants can do all. But it is my duty to do, when I have it in my power. 
 
"We lay hands on the sick and wish them to be healed, and pray the Lord to heal them, but we cannot always say that he will." 
 
Source: www.lds.org/manual/teachings-brigham-young/chapter-34