First of all, hello everyone!
Traditionally conceived, instruction in musical composition (in "classical" music, anyway) rests upon the disciplines of harmony, counterpoint, form and fugue. To get a good grounding in compositional techniques, you'll need to study each of these disciplines thoroughly.
All of Schoenberg's textbooks, including his Fundamentals of Musical Composition (Faber, expanded from his earlier pamphlet, Models for Beginners in Musical Composition) are eminently worth reading, but I would not recommend them unreservedly to "beginners in musical composition".
A better course of action, I think, would be to defer reading them until one has read (and worked through) some more recent textbooks on harmony, counterpoint, form and fugue.
Harmony Textbooks:
This is a vast field. At school I was instructed from C. H. Kitson's three (slim) volumes of Elementary Harmony (written and published in the early 1920s, these were still just about lingering on in the early- to mid-70s), and the first harmony textbook I actually owned was Stewart Macpherson's Practical Harmony. (Having decided to become a composer in my teens, I followed the advice of Aaron Copland in one of his books - probably What To Listen For In Music - in deliberately pursuing instruction in harmony and counterpoint.)
In my late teens I discovered the music, and some of the textbooks, of Schoenberg, including Structural Functions of Harmony, Preliminary Exercises in Counterpoint, and Fundamentals of Musical Composition. I already knew of his The Theory of Harmony by reputation, but it was too big and expensive for me to buy for myself (and I erroneously thought that it had been summarised in, and superseded by, Structural Functions in Harmony). (Eventually my parents bought me The Theory of Harmony, for my twenty-first birthday, and I belatedly studied this remarkable book.)
At about the same time I had found a copy of King Palmer's Teach Yourself Orchestration, which directed me towards Walter Piston's far larger and more detailed Orchestration, and thence to his Harmony and Counterpoint textbooks. I had also acquired from secondhand bookshops some of Ebenezer Prout's highly detailed textbooks (written in the late 19th century): Harmony - Its Theory and Practice, Counterpoint - Strict and Free, Double Counterpoint and Canon, Musical Form, Applied Forms, Fugue, Fugal Analysis and The Orchestra (this last in two volumes).
Fine as all these books mostly are, I would advise a beginning student of composition to work through one or other of two modern harmony textbooks, viz. Robert Gauldin's Harmonic Practice in Tonal Music (W. W. Norton & Company, New York, Second Edition, 2004) or Edward Aldwell and Carl Schachter's Harmony & Voice Leading (Thomson Schirmer/Wadsworth, Belmont CA, Third Edition, 2003). Both are excellent, but Gauldin's has the added advantage of coming with a CD-ROM containing many of the musical examples.
Counterpoint Textbooks:
As with Harmony, this is a crowded field. As a young man I was lazy, and wanted to learn a sufficient amount of counterpoint as quickly as possible, and so I bought (in addition to the bigger textbooks of Schoenberg, Prout and Piston) such outlines as R. O. Morris's Introduction to Counterpoint, Eric H. Thiman's Practical Free Counterpoint and Ernst Krenek's Tonal Counterpoint in the Style of the XVIIIth Century (which, fascinating as it is, does not teach a technique that any 18th-century composer would recognise as characteristic of the time).
However, there's no substitute for real hard work. Eventually I forced myself to go back to Prout and Schoenberg (and the earlier edition of C. H. Kitson's The Art Of Counterpoint). Had it been available to me at the time, I would have saved myself a great deal of trouble by first studying Felix Salzer and Carl Schachter's Counterpoint in Composition (Columbia University Press Morningside Edition, 1989). As a preliminary to Schoenberg and Prout, this teaches all the basic contrapuntal technique you are likely to need.
(An intriguing book on more modern contrapuntal technique, Bernhard Ziehn's Canonic Studies, was reprinted by Kahn & Averill in 1976. This book, originally published in Chicago in 1912, is known to have been influential on Bartok, but I also think that Franz Schmidt must have studied it.)
Musical Form:
There are two widely-used textbooks of musical form: Stewart Macpherson's Form In Music (Joseph Williams) and Douglass M. Green's Form in Tonal Music (Holt, Rinehart and Winston). The former is more familiar in Britain, while the latter is better-known in America. Both are good presentations of the subject.
(Schoenberg's Fundamentals of Musical Composition can also be regarded as - in part - a textbook on musical form.)
Fugue:
There are two outstanding studies of fugue:
i) Fugue by Roger Bullivant (Hutchinson, 1971);
ii) The Technique and Spirit of Fugue by George Oldroyd (Oxford University Press, 1948 with many reprints).
The Bullivant does not purport to teach you how to compose fugues (or even fugal expositions) but still contains a vast amount of useful information. The Oldroyd does offer a practical course in fugal composition, using the two volumes of Bach's Well-Tempered Clavieras its authority.
There are also Ebenezer Prout's Fugue and Fugal Analysis (Augener), highly detailed late-19th century textbooks, and Alfred Mann's The Study of Fugue (a compilation of fugal writings by such authorities as Fux, Marpurg, Albrechtsberger and Martini).
Books on Musical Composition, per se:
There are famous 19th-century treatises on musical composition by Czerny and A. B. Marx (the inventor of the term "sonata-form") that I confess I have not read.
One famous 19th-century textbook that I have read is Charles Villiers Stanford's Musical Composition (Macmillan/Stainer & Bell). This small book can be dipped into and returned to as one's command of the basic techniques grows.
Schoenberg's Fundamentals of Musical Composition is a very brilliant book, founded on a profound knowledge of 18th- and 19th-century repertoire. It would certainly be most useful to someone who already has the kind of harmonic and contrapuntal knowledge presented in Gauldin (or Aldwell and Schachter), and Salzer and Schachter, or, indeed, in Schoenberg's own Theory of Harmony and Preliminary Exercises in Counterpoint. (You'll also need access to scores of the earlier Beethoven Piano Sonatas, among others.)
The Composer and His Art by Gordon Jacob (OUP, 1955) is an intriguing read, if you can find a copy of it.
Although I am not hugely enamoured of most twelve-note music, I have a curious soft spot for Serial Composition by Reginald Smith Brindle (OUP, 1966). (Some years late Smith Brindle wrote another, more general book, Musical Composition (OUP, 1986), which, while a little thin, is certainly worth glancing at.) Schoenberg himself never compiled a complete textbook on 12-note composition, but there are Josef Rufer's Composition With 12 Tones (Barrie & Rockliffe, 1954) and George Perle's Serial Composition and Atonality (Faber, 1962).
Schenker:
The field of Schenkerian study is vast. The best general introduction is probably still Analysis of Tonal Music by Allen Cadwallader and David Gagne (Oxford University Press, New York, 1998), which supersedes and replaces Allen Forte and Steven E. Gilbert's often confusing and infuriating Introduction to Schenkerian Analysis (W. W. Norton, 1982).
Study of this will lead to Schenker's own writings, including the famous Five Graphic Music Analyses (reprinted by Dover Publications), Harmony, Counterpoint (in two volumes) and the celebrated Free Composition (in two volumes).
Bach and Beethoven:
Bach compiled his keyboard collections The Well-Tempered Clavier and the Two- and Three-Part Inventions as much to teach musical composition as to impart keyboard technique.
If Bach's Well-Tempered Clavier is the Old Testament, then Beethoven's Piano Sonatas are the New Testament. It's also essential to know Beethoven's String Quartets. There is a cheap Dover reprint of all the Breitkopf & Haertel scores, and a budget-priced CD box-set on Nimbus featuring the Medici Quartet. There are studies of these amazing works by Joseph de Marliave, Daniel Gregory Mason, Joseph Kerman and (in The Beethoven Quartet Companion (University of California Press, 1994)) Michael Steinberg.
Good luck!
