How simple-minded, exactly?
I haven't read any of Seirawan's Winning Chess series books, but a lot of people like them. The most basic one of his is "Play Winning Chess".
I have read Patrick Wolff's "The Complete Idiot's Guide To Chess", and I liked it very much. It doesn't get too deep into any one area. It just gives you a starting point in a number of areas. The writing style is geared more towards an adult or maybe an older teenager. A child or young teenager might have a little trouble understanding the somewhat adult style of writing. (Dan Heisman recommends the book for beginners over the age of 10.) Here's a new review of the book -
Edit - Also, if you want to consider more books, here's Dan Heisman's list of recommended books for different skill levels.