At the most basic level, if the Bible contradicts evolution, logically, one of them must be at least partly false. On the other hand, if they don’t contradict, they’re compatible and can be brought together. I’m going to suggest a way of approaching Genesis that I believe is compatible with evolution—but I don’t pretend that this is a complete “reconciling” of the two. Please feel free to ask more specific questions.
The Bible (in Gen 1–3, approximately) describes creation in very non-scientific language. The most simplistic interpretation of those chapters is that the world was created in a few steps, roughly in its current form. Obviously, that’s nothing like the mainstream theories of biological evolution.
However, we are meant to have to work hard to interpret the Bible correctly (Matt 13), so it’s perfectly reasonable to suspect that a simplistic interpretation entirely misses the point—especially if a large body of evidence contradicts it!
Consider what those chapters of Genesis needed to achieve*. Every person, from every culture, religion, and educational background, needs to get some meaning from Gen 1, even if it was simplistic! It couldn’t be long or technical, or seem implausible to scientifically uneducated people.
Genesis drops some obvious hints (every reader, from every time, could pick them up) that tells us that it is not the complete story of the origin of human beings. (Who did Cain marry? Who was he afraid of?)
The early chapters of Genesis are highly symbolic and invite us to look at as something like a parable, and find social and moral interpretations. For example, what is meant by the six creative days, in two cycles of three? What can people learn from the idea of the all-powerful God “resting” (see Ex 20:10)? What is meant by the first man being called “man”?
So, to bring the Bible and evolution together, you need to consider what the Bible is really trying to achieve. It’s a message about a good God, who created the universe because he takes pleasure in goodness. That’s a message that can be brought together with evolution (though I’d understand if you had follow-up questions!)
*As well as the positive lessons I’ve suggested, Gen 1 contains some negative implications. For example, it contradicts the idea of multiple gods, by speaking of one (good) God, working with a single purpose, to create a world that showed his goodness in so many ways. It opposes some competing ideas, for example, that the sun is a god. (Notice how oblique the reference to the sun is, in 1:16. It’s not even mentioned by name.)