The book that really got me going was The Way of Zen by Alan Watts. I felt like that was a good introduction for myself (a Westerner who didn't want the religious component of Buddhism).
From there it was pretty much a lot of sitting, breath meditation, and hard work - it's very tempting to chase thoughts that pop-up during meditation, but reminding yourself to let it go and move back to focusing on the breath builds the ability later in "everyday" life to notice you have a poor/misguided thought pattern motivated by ego or emotion and to step back and realize you are not that emotion or thought, it is just something happening, and you're able to let those emotions go much easier and make calmer and more rational decisions. I am in no way an expert of any sort, I'm still figuring out this stuff as well, but it's been significantly beneficial just from the short time I've been practicing.
Honestly the /r/meditation FAQ has some good resources and links there, especially ones relating to mindfulness in plain English (it cuts out the spirituality aspect quite a bit). There is also a course on Coursera called Buddhism and Modern Psychology ( https://www.coursera.org/course/psychbuddhism ) that I was interested, but I have no experience with it. Hopefully this helps in some way :-)
Here is a great talk about it from a doctor withouth any new age babble. He gives very simple advice and even backs up his claims with some research.
The gist of it is:
- For 15 minutes a day sit down and try not to think/observe your body/observe what is going on in your dead
- Do this for 30 days, after that your brain should pick it up and do it more or less automatically
