When Christians talk about the problems we see with science and religion or faith, they seem to fall into two main categories.
One is the story of creation. The scientific picture of the world, with what we call "the Big Bang" and evolutionary theory, is definitely at odds in many ways with the creation stories from Genesis. Cosmology, archaeology and geology all describe for us an Earth that's something like 4 billion years old and a universe that's as many as 15 billion years old. But Genesis leads us to a picture of an Earth that is several thousand years old, and those two numbers are not close enough together for the difference to be a rounding error. There are many people, in fact, who reject Christian teaching because of this difference.
When we look more closely at the stories, though, we can learn some things that might make it easier to accept parts of both understandings (you can tell I'm a Methodist -- if there's a fence within 500 miles, I will find it and sit on it). The Genesis creation account shares a lot of features with stories from people who lived in that part of the world at that time. Many of them feature a world in which primeval waters of chaos were divided by a divine being, with land appearing to separate the seas from one another. The Babylonian story is one of the major ones, and we find them sharing many details with Genesis.
But they are also different. In the Babylonian story, the earth and seas appear when the king-god, Marduk, defeats his mother Tiamat in battle. The earth is her dismembered corpse, and the seas are her blood. Quite a bit different from Genesis, in which we see God choose to create the world and bring order from chaos instead of more destruction. The point of the story the Israelites told was less to describe the physical creation of the world than the meaning behind the creation of the world. They used the science they knew to show the how, and then used what God revealed to them as the why, which was far more important to them.
Even the creation of people shows this. For the Babylonians, Marduk created human beings from the dust of the ground and breathed life into them, just as Genesis tells happened with God and the first human. But Marduk created people so the gods would have slaves and something to make fun of. God created human beings so his great love would have an object other than itself. God created Adam and Eve, but Marduk created Moe, Larry and Curly.
When we talk about the beginning of the world today, we hear a lot about the random chance of it. How the Big Bang itself was a random event, and the formation of the world happened in the right spot by chance, and how the laws of the universe are what they are by random chance, and so on. But as a Christian, I see God's hand in these things. Because of that hand, we have a world in which beings exist that can respond to God and love him back.
The other wrinkle with science and religion is this idea that we must pick one or the other; that there can be no overlap and no agreement. Christians must reject science because science, of course, rejects religion and Christianity. But they don't. Many scientists find what they learn about God's world deepening their faith. Physicist John Polkinghorne retired from work at a university and went back to school to become a minister in the Church of England. I have a friend who teaches pediatric pharmacology (you can tell who's smarter by the number of syllables in her job and the number in mine -- pediatric pharmacologist vs. preacher). She sees the cutting edge of scientific work in the arena of the human body itself, and both her research and her practice bring her closer to God.
I myself accept a lot of what science tells me about how the universe came into being and how the people who live here developed. But that doesn't mean I reject faith, because it's my faith that helps me understand why the universe is here and why people who can respond to God are here. And that, for me, is the key. Have all the fights you want about how everything came to be. Argue it, hash it out, fuss about it from now until the second coming, but don't pretend you've done what needs to be done as people who think seriously about the world and the human condition unless you've got some kind of an answer as to why.