You CANNOT learn ASL from a book. No one has figured out a way to show how signs really look on a two dimensional page. Spoken words, without gesture, expression, or tone, are two dimensional. Signs are three dimensional. Real English cannot be written either. Only the spoken words that comprise the written language can be written. It is the tone of voice, facial expression, and body language that give the words meaning.
You can learn ABOUT ASL from a book. There is a lot to know about ASL that is not contained in the signs directly -- And which do not seem to be understood by some of the "lexicographers" who are "adding" words to the dictionary. For example I recently saw the word "healthy" initialized and signed moving downward. Anyone who understands ASL knows that downward is negative, mysterious, or unknown. In order to mean "healthy", "happy" or "well" the sign MUST move upwards.
You can learn a lot of ASL from DVD's. You can learn vocabulary, correct ways of making the signs, and build your receptive skills.
But: As soon as you are not using your skills with and around Deaf people your communication skills start to deteriorate.
This is from experience.