"Algorithms + Data Structures = Programs" by Niklaus Wirth: http://www.amazon.com/Algorithms-Structures-Prentice-Hall-Au...
While example programs are in Pascal programming language (that the author created), it is still a very well written book that teaches how to connect real world problems to programming from a beginner's standpoint. It assumes the least out of the reader of nearly all programming books I know of. Check out the reviews at Amazon.
[1] My story: I started programming at the age of 11 when my father gifted me a computer, and its manual. That manual was so concise and precise that I learned something new from it each time I read it. It ended with a chapter on writing machine code, which led me to write short programs in machine code straight by age 15!
I took a look at the online second edition (and I happen to have a hard copy of the first edition in my library). I like the book and believe that it is one of the best books I've seen for teaching a beginner to program. The subjects covered are non-trivial, but the book gets the students there in a well paced presentation. The book emphasizes the importance of breaking down problems into well defined parts, defining the interfaces, and implementing each part as a function that satisfies the desired contract.
If you are an experienced programmer, I believe that your time would be better spent on a book that is less oriented around teaching the basic steps that you already know. Books that I can recommend to experienced programmers interested in advanced subjects in programming:
1) Structure and Interpretation of Computer Programs, 2ed., by Harold Abelson, Gerald Jay Sussman, Julie Sussman. This book will teach you how to program in Scheme, and you will learn much more than just the syntax. I would consider this to be a very demanding book for a complete beginner. Available online: https://mitpress.mit.edu/sicp/full-text/book/book.html
2) The Science of Programming (1981), by David Gries. This book and the smaller, but equally difficult monograph The Discipline of Programming (1976), by Dijkstra are great books but too hard and mathematical for many readers. They focus on verifying the correctness of programs and introduce a formalism that shows how the logical effects of each program statement can be combined to prove that the program satisfies its specification. There are practical limitations not addressed by these early expositions on program correctness, but the techniques covered can be applied by hand and I've often used them on especially troubling passages of code that I wanted to make sure were correct. If you are up for it these books will introduce new ways of thinking about your code. I'd advise taking a peek at the books before buying to make sure it will be worth the investment; it definitely was for me.
3) Learn You a Haskell for Great Good!, by Miran Lipovaca. Like learning Scheme, learning Haskell will teach you about a new way of thinking about programming. This is a nice introduction to the language. Even though I'm still trying to learn Haskell, this book was my favorite of all my books on Haskell (I've got all of the ones written in English). Learn Haskell to understand where researchers are exploring the possible futures of programming. This book is also available online: http://learnyouahaskell.com
4) Algorithms + Data Structures = Programs (1976), by Niklaus Wirth. This book is far easier on the reader than the ones I've listed above; I've included this book because it is just a fun read for any programmer. It's old and uses Pascal, but it still a great book on programming that introduces a number of algorithms and data structures. It's available used for reasonable prices: https://www.amazon.com/Algorithms-Structures-Prentice-Hall-A.... For a more advanced introduction to data structures I suggest MIT's Open Courseware videos taught by Professor Erik Demaine, https://ocw.mit.edu/courses/electrical-engineering-and-compu...