Familiarize yourself with basic sheet music notation, such as time signatures and clefs. The time signature is represented by the two stacked numbers on the left of the staff. The first number represents the number beats in a measure, and the lower number indicates what type of beat the first number is referring to. Most commonly, jazz music will be written in 4/4 time, though there are many exceptions.
Learn to read bass clef music. The vast majority of jazz music played on the trombone will be written in the bass clef. The names of the notes placed directly on the bar lines, from top to bottom, are a, f, d, b, and g. The notes in between the bar lines are g, e, c, and a.
Understand the length of notes. A hollow circle placed on the bar line will indicate a whole note, equal in length to four quarter notes. This same circle with a vertical tail indicates a half note, which is half as long as a whole note. Eighth notes have a short horizontal tail connected to their vertical tail, and are filled in like quarter notes.
Look through your sheet music to find notation specific to the trombone, such as a glissando. This will look like a line connecting the body of one note to another. A glissando indicates that you should gradually shift the pitch of one note to the next. Do this by blowing through the trombone continuously as you adjust the slide.
Learn to "swing." Most jazz music is played with a swing feel, even if it isn't directly indicated in the sheet music. This will give the music a relaxed, loping feel. Learning to swing properly isn't something you can learn from a book; listen to jazz recordings to get a feel for how different trombone players use this technique.