For guidance on such matters, Muslims turn first to the Qur'an. Allah gives us general guidelines to follow, that are constant and timeless.
The Saving of Life
"...We ordained for the Children of Israel that if any one slew a person - unless it be for murder or for spreading mischief in the land - it would be as if he slew the whole people. And if anyone saved a life, it would be as if he saved the life of the whole people...." (Qur'an 5:32)
Life and Death is in Allah's Hands
"Blessed be He in whose hands is the Dominion, and he has Power over all things. He who created death and life that He may test which of you are best in deed, and He is Exalted in Might, Oft-Forgiving." (Quran 67: 1-2)
"No soul can die except by Allah's permission." (Quran 3:185)
Human Beings Should Not "Play God"
"Does not man see that it is We who created him from sperm. Yet behold! He stands as an open adversary! And he makes comparisons for Us, and forgets his own creation. He says who can give life to (dry) bones and decomposed ones? Say, 'He will give them life who created them for the first time, for He is versed in every kind of creation.'" (Quran 36: 77-79)
"Kill not your children on a plea of want. We will provide sustenance for you and for them. Come not near shameful deeds whether open or secret. Take not life which God has made sacred except by way of justice and law. Thus He commands you that you may learn wisdom." (6:151)
"Kill not your children for fear of want. We shall provide sustenance for them as well as for you. Verily the killing of them is a great sin." (17:31)