Death is a part of life. As Ecclesiastes 3:2 tells us, there is a time to be born and a time to die. The wise among us should number their days (Psalm 90:10). A Christian can even welcome natural death knowing that "death has been swallowed up in victory" (1 Corinthians 15:54). Who doesn't look forward to that day when we meet him face to face?.
Therefore in looking at suffering and impending death the Christian should see God's sovereign hand and purpose, as well as the opportunity for ministering to the weak and vulnerable, with whom Christ himself is identified.
This effectively is just trying to say that human life is sacred and valued by God; it should be sustained whether in pain or sickness. Christians also believe that death isn't the end of life as we know but only the beginning and that those with faith will share in a bodily resurrection like Christ. Therefore Christians have a duty to ensure the elderly face and grow old gracefully enduring the wrinkles and the sickness with confidence and dignity. For Christians this means that human life regardless of age, health etc should be protected right up until the end.
Euthanasia simply means "Easy Death". In the declaration on Euthanasia it says: Ultimately, the word "euthanasia" is used in a more particular sense to mean "mercy killing", for the purpose of putting an end to extreme suffering, or having abnormal babies, the mentally ill or the incurably sick from the prolongation, perhaps for many years of a miserable life, which could impose too heavy a burden on their families or on society. This is just a definition of Euthanasia but in my opinion if you are willing to create a life then you need to be willing to accept the circumstances of life.
Apart from the bible Christians also look to the leaders of their church to guide them. For example in the Roman Catholic Church, look at Catechism of the Catholic Church. The Catechism shows us about Christian beliefs on their responsibility for those at the beginning and end of their life.