Begin your musical journey with a good music theory text. With the proper textbook, you will learn music theory quickly. Look for a textbook that discusses notes, note values, key signatures, scales, chords and chord progressions. Each of these subjects is required to write sheet music. A good text for studying theory is Stefan Kostka's "Tonal Harmony."
Study counterpoint after you have a solid understanding of music theory. While theory will teach you about chords and progressions, counterpoint will teach you about proper voice leading. Voice leading is essential to creating quality music and balanced musical lines. With proper voice leading, a composer can make even extreme dissonances sound palatable to the ear. Voice leading is the key to writing melodious and error-free chord progressions. A good text on counterpoint is Fux's "The Study of Counterpoint."
Start writing the melody of your piece first. The melody is going to be the element of the composition that dictates what chords you should use. Most melodies are about four measures in length.
Write the chord progressions underneath the melody. You should start with a tonic chord. For instance, in C major you would want to start with a C major chord. Once you have the initial chord written, you can continue to add chords that fit the melody. Check to make sure that the chords you use have a common tone with one of the notes in the melody. You should avoid writing a D minor chord with a melody line that has an E. The D will conflict with the E. Use mostly stepwise motion and avoid having all of the lines move in the same direction to achieve decent voice leading.
Add a bassline to the composition. The bass does not have to worry about moving by step. It should be interesting and melodic. Many composers refer to the bass as the second melody since it often is much more active than the other voices.
Create a second draft of your composition. The second draft should include passing tones that move between the chords and help to spice up the chord progressions. Consider using suspensions to help create more interesting voice leading. A passing tone is a tone that is not part of the chord and is used as an intermediary note between two chords. A suspension occurs when one note holds over into another chord before resolving down by step.
Edit the composition and include dynamics, phrase markings and tempo indicators. These are important parts of any composition. If the composition does not have these markings, the piece is incomplete. Dynamics tell the performer how loud or soft to play; phrase markings help to indicate how to phrase the piece; and tempo lets the performer know how fast or slow to play. Additionally, articulations should specify how to play a note -- short, legato, long or accented.
Create a final draft of your music to prepare it for publication. Use a ruler to make sure that the lines between all of the staves are straight, and make sure to space each note relative to its note value. For instance, there should be enough space between a quarter note and the next note to fit two eighth notes. You should be able to fit four eighth notes between a half note and the next pitch.
Study further and continue to improve your skills by studying instrumentation, orchestration and form. These advanced subjects will help you to write for instruments and create compositions that have a logical structure.