The book that I use in my beginners' classes is Bridge For Dummies by Eddie Kantar. For a while I taught using the ACBL series of books, but Kantar's book covers in one volume what the ACBL series takes five books to cover, making the Dummies book a much more economical buy. In addition, Kantar is funny (in this and every book he writes); the ACBL authors are not. I think the only respect in which the ACBL series is superior is that is has quizzes; the Dummies book does not.
There are two basic pedagogical schools of basic bridge instruction: "bidding first" and "play first." Dummies is a "play first" book, but I don't teach it that way. I skip around. I'll put the reasons in a footnote1 for anyone who's interested, and you can get my syllabus by clicking here.
There are also a couple of free computer programs (Windows only) that teach bridge to beginners. They are available here. (Don't be too concerned that the approach to hand evaluation take by these programs is slightly different from the method described in the Dummies book. Just pick one method and stick with it.)
The first thing you need to work on is your declarer play. My recommendation for that is William Root's How to Play a Bridge Hand. Don't be concerned that the book is more than a decade old. Declarer play, unlike other aspects of the game, does not change over time. Master this book and you will declare better than 90 percent of the players at your club.
You can't learn to defend well until you know how to declare, for the simple reason that you won't know how to thwart declarers until you know how they succeed. After you've gotten a handle on declarer play, I recommend How To Defend A Bridge Hand by William Root.
Again, don't be concerned about the age of the book. Almost nothing has changed since the book first appeared more than a decade ago, and in fact Root recognized (and recommended) the one change that has occurred2 and addresses it at the end of the book, so the book is as useful today as it was when it was first published.
Unfortunately, How To Defend A Bridge Hand appears out to out of print now, although used copies can be purchased at the link. If you would like something newer (and currently in print), I recommend Eddie Kantar Teaches Modern Bridge Defense. And after that, you should work your way through Eddie Kantar Teaches Advanced Bridge Defense.
One of the first things you're going to hear when you start playing with better players is "You should be playing two-over-one." I don't know why there isn't a good beginners' book that starts immediately with two-over-one ("2/1"), but there doesn't seem to be one.3 In fact, I'm not sure there is a great introductory 2/1 book even for those who already know standard bidding. I think the best 2/1 book is Mike Lawrence's Workbook on the Two Over One System, but the drawback to it is that it assumes the reader has some understanding of 2/1 to begin with and is just trying to improve on that understanding. If you already have some understanding, this is the book for you.
If you don't already know the basics of 2/1, I'd recommend one of the following:
Let me try to steer you away from any 2/1 book written by Max Hardy (Two Over One Game Force, Standard Bidding for the 21st Century, Modern Bidding for the 21st Century). Every example hand in Hardy's books works well with the system he describes because he avoids all the hands that don't quite work. Every bidding system has some weak spots, and the better writers discuss what to do with "problem hands"; Hardy's books pretend problem hands don't exist. In addition, Hardy never lets the reader know that many of the things he specifies as part of "the 2/1 system" are the subject of disagreement among experts. In fact, many of the treatments Hardy specifies are not in accordance with majority opinion (as expressed, for example, in polls by Bridge World Magazine). Mike Lawrence is much better about presenting alternative treatments and telling you why he recommends the one he does. Finally, Hardy's prose is just awful -- a struggle to get through.
Whether you adopt 2/1 or not, you'll serve yourself well by reading the following books, in approximately the order given. They are all by Mike Lawrence:
Lawrence has summarized the more basic parts of the five books listed above in two books, Tips on Bidding and Tips on Competitive Bidding. You could substitute those two for the five above if you're willing to sacrifice some details.
In addition, there are a number of conventions you should add to your bidding repertoire -- or at least understand when your opponents use them. 25 Bridge Conventions You Should Know is a good place to start learning them.
Another one by Mike Lawrence: Opening Leads. There is much more to know about opening leads than you will have learned in your beginner's book.
Got a question about any bridge book? I own an extensive library and have probably read any book you might ask about. I'm happy to answer any questions. Just email me at email@example.com.
1 When a deal of bridge is played, the bidding comes before the play of the cards. The "teach play first" school argues that one must know what is involved in playing a contract before one can understand how to bid to that contract. How can beginners understand what a hand is worth if they don't know how tricks are won? The "teach bidding first" argues that since bidding comes first at the table, it's logical to teach it first. I think the "teach play first" school has the better of the argument, and if I could teach bridge only to those 100 percent committed to learning, that's how I would teach it, following the Dummies book in order. But the truth is that almost no bridge student is 100 percent committed; nearly all of them are just dipping their toes in to see whether they like it. If they're taught "play first," they can't go home after one of the early lessons and try to play with friends. Students need to learn a little of bidding and a little of play at each lesson. That's what I try to accomplish in teaching according to my syllabus.
2 The change involves what to lead from AK on opening lead. When How To Defend A Bridge Hand was published, most players led K from AK, but most experts were by then leading the A. Now the A is standard even for beginners (as Bridge For Dummies teaches).
3 There are some books that purport to teach 2/1 to beginners, but I haven't seen a good one. And I'm pretty sure I've seen them all.