Big Java by Cay Horstmann is the textbook my school is using for our AP Computer Science class, and I think it is a simple and thorough introduction to computer programming in the Java language. The book starts with a basic overview of programming and moves into more complex topics at a managable pace.
Throughout each chapter there are "Self-Check Questions" to make sure you are completely understanding what you're reading. Horstmann also provides explanations as well as examples illustrating important Java concepts. Many of these examples are full programs, which you can use to check your comprehension of the topic.
This book is great for a classroom setting, as well as just learning Java on your own. The language is witty and entertaining at times and easy to understand. With this book, you'll be a fluent programmer in no time!