Amazon has many good flash books. Some are "system" books which explain the buttons on a specific flash. My own notion is that the better books explain how take good pictures. Most have pretty high satisfaction ratings from customers. In the top-most choices there, there are a couple that seem required in any beginning library.
Beginners to photography: Bryan Peterson's Understanding Exposure, 3rd Edition: How to Shoot Great Photographs with Any Camera has become THE classic about beginning photography. This book does Not cover flash. Specifically, it is about the basics of using shutter speed and aperture. Definitely a beginning level book, for newbies, but this is what photography is, and we absolutely gotta know this most basic stuff. This book should be any beginner's first photography book, to start them down the road in the right way. It is not deep - it is a very easy read about how the first basics of photography work, about using shutter speed and aperture for exposure. This one has developed a wonderful reputation about being very effective to get beginners started right, they like it. There is more to its subject than just "Exposure" - it is about the Whys of your choices. When you know why, you know how. However, this one is NOT about flash. This book is about regular continuous light, sunlight and light bulbs, about everything EXCEPT flash. Be aware that flash is quite different, in a few ways, and we must know both. But if aperture and shutter speed are still any mystery, you need this one before all else. This book will very likely be in your public library (may be a waiting line for the new third edition, but the older ones are good too). Only about $15, and if you need it (and every beginner does), then this is easily the best money you can spend on photography.
As useful as the above book may be, I might skip past Peterson's new Understanding Flash Photography: How to Shoot Great Photographs Using Electronic Flash.
It is a pretty good beginning introduction to flash for manual flash, if you wish to work that way.
Its noticeable fault (for beginners) is that it totally rejects TTL flash mode in favor of manual Guide Number flash mode. And even that coverage is dumbed down, the book never even explains Guide Number (covered here). Guide Number is a very decent system, but only for bare and direct manual flash mode, if you know the distance. Meanwhile, the rest of us are enjoying TTL bounce flash. The GN/TTL differences are:
You can always compute direct flash exposure with guide numbers, or tweak manual results by eye, or use TTL. The book ignores TTL, and says the reason is because TTL can be affected by the subject's colors, and so is not always precisely accurate or reliable (which of course, the same is always true of the camera's reflected meter reading). But it never mentions flash compensation, which we need to know is how we control TTL flash exposure. And yet then, the book's exposure instruction given for bounce flash is to "open the lens two stops"? (from the direct flash value.) That was a standard ballpark guess 50 years ago, for flash bulbs before electronic technology (and using negative film which had very wide exposure latitude), but this guess is far from accurate enough for digital, certainly not like TTL actually metering the flash could be. He admits any small softbox will reduce the flash by "about a stop", and same for a gel filter. So you're back to determining exposure by trial and error. This part is pretty weak today, and bounce and umbrellas are extremely more important than was acknowledged here. This book is full of many full page pictures (space fillers), but for beginners, just reducing the size of a couple of them could have allowed space for a quite a few words about using TTL and flash compensation.
Still it is a good read with colorful pictures (faint praise maybe), and yes, the book is a decent introduction in other ways, and much of the rest of its ideas are good ideas that can be useful even if you use TTL. It is about flash, but just know that this book does NOT include TTL use.
When you are ready for "the next book you really need", Neil van Niekerk's On-Camera Flash Techniques
is a great book about "using" flash - about using one hot shoe flash to create good lighting to take great flash pictures (which should interest everyone, that's what flash is about of course).
Note: A newer version is coming November 2015
No qualifications about this book at all (OK, it is really not for rank beginners with zero photography experience). It is for anyone seriously interested in improving their flash pictures. The subtitle does say wedding and portrait photography - Don't let that scare you off, it is just about "flash". But it is a serious book (an easy read, but no fluff), and if you want to know how to use your hot shoe flash to take great flash pictures with good lighting, this is it. Snapshots or serious work, these methods will enhance any flash picture you take. Real world, and as good as it gets. On-camera flash is about bounce flash of course, but it covers most things about flash usage - metering, color balance, flash modes, TTL and compensation, flash with tungsten ambient light, fill flash in daylight, etc. If you do want to know, this is that stuff you want to know about using on-camera flash.
Neil's newest book is Direction & Quality of Light: Your Key to Better Portrait Photography Anywhere, obviously proving to be a big hit. This covers speedlights in many situations, both bounce and off camera, including multiple lights.
Neil also provides much information on his excellent web site. If you want to know how to improve your flash pictures, see the extensive blue column menu at right on his page. Good flash lighting is greatly easier than you may think, but realized only after you actually try it, and start getting the idea about the basics.
This one is about taking the portrait picture in the studio situation. Steve Sint's Digital Portrait Photography: Art, Business & Style is excellent, packed with actual practical information. Lighting is covered, but the real meat is the strong section on posing, including groups, in a useful way that helps. An older book (2009), but it is very impressive, both in content and price. Books like this are also available used, from vendors via Amazon, for maybe $5 including shipping.
There are many books about portrait photography, of which I have too many. Some didn't do much for me, but several are pretty good. I also like the books by Bill Hurter and Monte Zucker, which seem like classics. But we do need to see more than one. The one that has easily impressed me the most is The Portrait: Understanding Portrait Photography by Glenn Rand and Tim Meyer (of Brooks Institute). This book is rather different than the others, being more detailed about the theory, instead of about the equipment. It does have specific explanations of the basics about the lighting. Each point is carefully explained. It assumes you actually want to know, and it actually says the words! So a little wordy perhaps, but clarifying, not rambling - it is a very comfortable read. A few extra words seemed a big plus to me.
Other books may be a more conventional first introduction for beginners (who don't have the questions yet), but following that, then this one is different, and if you have ever tried to set up a lighting session, you should recognize the issues here that you still wondered about. This book actually explains portraits to me, because it explains the why's of the lighting, in a way that creates understanding.
Other than satisfaction at last, a notion I had was that if there were going to be a written test, obviously this is the material that would be on it. This one seems more clear than any about the basics, in my mind, the actual answers are finally here, to be able to "get it".