Purchase a Jazz Fake Book. A Fake Book is like the Bible for jazz musicians. It contains the sheet music for almost every jazz standard. Study the elements of jazz songwriting, such as melodies, harmony, and tempo. The 32-bar structure is the most commonly used format in jazz. It typically is written in an "AABA" format, with each section comprised of eight bars. The 4/4 time signature is heavily relied on, but many jazz compositions are in 3/4 or 6/8 time, as well as more difficult time signatures, like 5/4 or 7/8.
Study jazz harmony. The harmonic and chord structure in jazz is more sophisticated than in other types of popular music. The most commonly used chord progression is "II-V-I" progression. Jazz compositions will often go through several key changes during the course of one song. The key to identifying the key is to recognize the "II-V" changes. For example, a D minor and G7 will tell you that you are in the key of C major. The ability to incorporate key changes in a song provides a bigger pallet of melodic ideas to draw from.
Find the right melody. Jazz songs, which may or may not have lyrics, are recognizable by their melodies. The songs that have become memorable standards are the ones where the melody matches the thematic content. Good examples of this include George Gershwin's "Summertime," Duke Ellington's "Take the A Train," and Thelonius Monk's "Round Midnight." In each of these examples, the melodic ideas evoke the particular mood that characterizes the song. The slow opening lines of "Summertime" capture the feel of a lazy summer night, while the syncopated melody of "Take the A Train" evinces a subway ride up to Harlem for a night out on the town.
Sketch out an outline for the song. Place the melodic idea within the 32- or 12-bar format. Experiment with different keys. Certain keys may work better than others in capturing the overall feel and mood you want.
Write an arrangement for the song. The final stage of writing a jazz song is to fine-tune it with an interesting intro and conclusion. Intros usually end on a "V" chord, which leads its way back to the "I" chord.