Check out Zen Mind, Beginner's Mind for a good book on practicing meditation. It's not religious, but basically a transcript of a Zen Master's talks on zen and the practice of meditation to his group of students. It's what I recommend to people who want to 'get' meditation.
Not specifically related to meditation, but The Tao of Pooh is still the best book I know of that deals with the concepts behind this stuff. I re-read these books whenever I lose my way, which happens more often than I'd like to admit ;)
I'm currently reading The Instinct to Heal by David Servan-Schreiber [0]. It's not specifically about mindfulness, but so far I found it everything to be what I was looking for when I was looking for writings on these topics. On the internet I've seen a lot of essays pass by about mindfulness, but they're all a bit alike. This book is interesting to me because it gives info about methods I didn't know about, and provides scientific data and references to base its claims.
[0] https://www.goodreads.com/book/show/153401.The_Instinct_to_H...
