Turn the computer on and open your music notation software. Keep in mind that although each program is a little different, learning one of them thoroughly makes it easy to figure out others in an intuitive way.
Enter the initial melody into the staff line of whatever instrument would be best suited to introduce the theme. Experiment with different chords or rhythms underneath the main melody. A common example would be to give a primary melody to a trumpet or saxophone, with the bass adding a secondary melody, and to have piano accompanying with chords or a repeating rhythmic pattern.
Consider the structure of the arrangement. A good arrangement will have a concrete beginning, middle and end. If the transitions between these sections sound vague or haphazard, the listener will become confused.
Listen back to the arrangement at a slower speed than it is intended to be performed. This makes it easier to hear small mistakes and to fix them.
Print out all the parts to the arrangement and check them for typos or any obvious flaws before distributing them to the musicians.