The quick answer to this question is “not at all”, but I’ll fill in some detail here. Hebrews 11:1 says: “faith is confidence in what we hope for and assurance about what we do not see”.
The faith of Christian is a faith in God. We are sure that He exists, even though we cannot see Him. We have confidence in all that He has said and prepared for us. And all that the Bible tells us about God, heaven and the future. We believe and are confident that it will be just as He has said.
God heals in miraculous ways
When we are sick, the first course of action is always to pray. The next step may be obvious, take a paracetamol for a headache, visit the Emergency Department for a broken bone, but some other problems may not be as easy to assess. God has placed us all in a world that is damaged and hurt by sin. Sickness, illness, even depression and finally death are things that we will all encounter.
In the Bible there were doctors. The most famous one is Luke, who traveled with Paul frequently and finally joined him on his trip to Rome. We know that Paul had an ailment from which he suffered badly and pleaded with the Lord to take it from him. The Lord answered “My grace is sufficient for you” (2 Corinthians 12:9). Undoubtedly doctor Luke cared for Paul when he was struggling. Besides treating this ailment, he probably helped with wounds from beating, advise when Paul was exhausted, and help in other ways. God heals in miraculous ways. But even so, there were sick people in the time of the apostles who needed attention from a doctor.
Doctors have been given God-given skills to help the sick and weak, whether they are Christians or not. Chemists and pharmacies have pills and medicine that God gave people the skill to make. When we are sick, God has given us common sense. And with the exception of some health problems, seeing a doctor is always a good idea. If you have a cold, or stomach problems because you overate, a headache from trying to work through the night and easily diagnosable problems, then common sense tells you to rest. And e.g. take some cold medicine. When it comes to health problems that you have no idea of the cause, then a visit to the doctor is common sense, wise and completely in line with the Bible.
Temple of the Holy Spirit
We may have prayed but may not know whether God will heal if he doesn’t heal instantly. Yes, some people have been miraculously healed in answer to prayer, but others have suffered pain, misery and even death by refusing to go and see a doctor and claiming “The Lord will heal me”. God has given us a body to care for the best we can. He calls it the temple of the Holy Spirit who dwells within us, and just like the priests and Levites of the Old Testament were given a solemn charge to care for the temple, we too have been given the charge to care for our bodies.
If you are sick, pray and go to the doctor. You do not know whether God chooses to heal you through the restoring powers of your body, through his miraculous intervention, or through the skill he gave to the doctor. Use everything, and thank him for your healing, whatever way God chooses to give it to you.