The relationship between faith on the one hand, and science and reason on the other, is not always easy. Here I'll look at how believers deal with the issues; in part 2 I'll examine how unbelievers go.
Religion is often seen as the enemy of science, with cases being quoted like Galileo's conclusions on astronomy being muzzled by the Catholic Church. But it also seems to be true that the Jewish, Christian and Muslim belief in a creator God and an orderly universe contributed greatly to the rise of the modern scientific method (see, for example, God's Philosophers and this discussion). Certainly it is true that, while scientific discoveries were made in many cultures, the scientific method flourished initially in Christian Europe, generally under Christian patronage.
But Darwin changed all that, and Christians have historically questioned, and even opposed, the theory of evolution. The opposition has sometimes been illogical and nasty, at other times thoughtful and apparently reasonable - e.g. the more thoughtful side of Creationism, and the Intelligent Design movement. But it nevertheless seems to be based on wrong assumptions and poor science.
Much of the opposition to evolution comes from the view that if the Bible's book of Genesis is interpreted literally, it is hard to reconcile it with the findings of modern evolutionary science. But this view of Genesis is not certain. As early as the fourth century, St Augustine, recognised as one of the great thinkers in church history, warned against a literal interpretation of Genesis; CS Lewis, one of the most influential and respected Christians of the 20th century, and a very learned man on historical literature, also felt no problems in interpeting Genesis in a non-literal way.
Scientifically, it seems that the majority of Christian scientists working in related disciplines accept the broad truth of evolution - that the earth is old and that life developed from simple to complex - even if they may quibble over some details (e.g. the creation of life), and certainly believe it has been a process set up and overseen by God. For example, the majority of members of the American Scientific Affiliation (an organisation of Christian scientists) believe science points to an evolutionary process.
So it seems many Christians still see faith and science to be opposed, but there is a growing number who see faith and reason/science has being complementary to their belief. (For my conclusions, see evolution and design.)
There has been a strong scientific consensus on the reality of human-induced global warming for some time (see maybe, just maybe, we're starting to get this right and climate change continues to bite in australia). Nevertheless, many conservative people and business interests, especially in the USA, have argued the the evidence is still uncertain. Some undoubtedly fear a reduction in business profits, but for others, Christian suspicion of science, generated by evolution, seems to have spilled over into discussion of global warming.
Here it seems to be less a matter of faith vs science, and more a mistrust of science (this commentary from 2005 is typical), and a preference to believe respected Christian spokespeople, as this report shows. This indicates a poor view of science and reason by some Christians, although it seems that this unfortunate situation is changing.
reasons to believe
Some Christians mistrust human logic and believe "on faith", but most would argue there are good reasons to believe (see, for example, ibelieve). Certainly "proofs" of the existence of God, from science, human experience and history, have a long history and books about them remain popular (e.g. Lee Strobel's The Case for a Creator and The Case for Christ). Whether one agrees with the case being made or not, the popularity of these and other books illustrates that reason, science and history remain important factors in the faith of many Christians.
Christians (and other theistic believers) have an ambivalent attitude to science and reason. Some are very critical, some are very committed to logic and evidence, and an increasing number seem to be seeing with one eye of reason and one eye of faith. If one believes that science and reason are good methods to arrive at truth (albeit not necessarily the only methods, or even the best methods in some cases), then believers still have some way to go, but appear to be moving in the "right" direction.