To get started, I read Mindfullness in Plain English [1], which is a pretty practical, no-nonsense guide with minimal New Age woo. It addresses a lot of the problems and questions a beginner will have getting started.
I can't really claim any long-lived effects or benefits of it. As I said, I'm very skeptical by nature, so I tend to be wary of attributing anything to it. One thing that's very clear and noticeable though is that I feel very mentally different during and afterward. My mind is quiet in a way that it otherwise never is, and I feel like I perceive the world differently somehow (maybe more clearly or more at face value.) It reminds a lot of a hyper-focused flow state, except it's non-directional. It's like I'm focused on everything and nothing all at once.
After I started, I did some reading on wikipedia and found that meditation has been found in scientific studies to have certain benefits and neurological effects. It's apparently even a treatment doctors recommend for handling stress and anxiety. That has helped me stick with it, because the meditation community is full of New Age bullshit. It's nice to know that there's more to it than that.