First, a remark on the title: this is not a companion to the program, but rather a companion to some other book on LaTeX you should have. I bought this book back in 1994, when it was the first book on LaTeX2e, and by now it is thoroughly worn (though the binding is still doing its job well :). However, at the time I bought it, I have already been using LaTeX for six years, and have read Lamport's guide (which is charming, and also the book The Companion intends to accompany) and Kopka and Daly's (which is better organized and more complete).
The LaTeX Companion is something between an advanced course tutorial (could just as well be named Selected Chapters from LaTeX) and a reference book. None of them was ever aimed at beginners, and this one is no exception. LaTeX comes with a rich legacy of add-on macro packages doing various useful and nifty things with lists, floats, tables, formulas, graphics, fonts, indices and bibliographies. This book covers some of them. I would love to see second edition of this book covering more of them. There is a treasure hidden at CTAN, but it is usually hard to find it. The examples are well chosen and it is easy to learn from them. I am less pleased with the index. At 36 pages, it looks very promising, but it rarely led me to the place I sought. During years of use, I mostly figured out where in a book things are, and stopped using it.
Despite the confusing index, the book is worth its (admittedly high) price and you will probably learn many useful things from it. The idea of a thin tutorial and a partly-overlapping "companion book" doesn't appeal to me, though. Personally, I would prefer one single book with a complete treatment of the topic.