My answers are based on my experience working on commercial products with relatively large budgets and therefore different in some regards to the answers you have already received. I leave it to you to decide how applicable my answers are (or are not) to your situation.
The two main professional workflows are roughly split into documentaries and dramas. With documentaries the composer is hired sometime around the start of post-production and supplied with a cue sheet detailing the music cues required. The composer creates the specified cues which the director either approves or provides a list of required corrections. With dramas, the composer is hired during pre-production and supplied with a script. After a period of time to study the script there is a meeting with the director where general questions are discussed such as: A detailed description of the genre, the target audience, the general motivations of the main characters, any points which are unclear or ambiguous from the script. From this info the composer can suggest/discuss/negotiate the musical genre which would be most appropriate. Before, during or just after production the composer would meet with the lead actors and discuss how they see and are approaching the characters they are playing, the character's motivations, mental state, etc. The composer would usually receive some rushes during production and would sometimes create some basic looped musical sketches which can be used by the picture editor as an editing aid in post-production. Another meeting would usually take place as soon as filming has wrapped (or even before it has wrapped) to review these musical sketches to make sure they are in roughly the same ball park as the director's expectation. Once picture lock has been achieved (and the composer has studied it) an in-depth spotting session/s would take place with the Composer, Editor, Director, Sound Designer and possibly Producer. The director and editor will usually have a rough list of locations where they want/think music cues would be appropriate.
As the composer I wouldn't expect the director to have a good understanding of music but I would expect them to have a good idea of how to use music. For example, with a music cue suggested by the director, why is the director suggesting a music cue at this point? There is usually a primary reason and one or more secondary reasons. For instance, a primary reason might be to plug a bit of a hole/aid the pacing and a secondary reason might be to help camouflage a clunky visual edit. I (the composer) would then ask a number of questions pertinent to the cue/scene such as: What is the primary emotional response you want to elicit from the audience? Are there any secondary responses/undercurrents required? Should the cue focus on/empathise with a particular character and if so why or should the cue focus purely on the overall situation? What are the precise character motivations you would/would not like the audience to be aware of? Should the cue confuse or simplify the plot, should it make any reference to an event which has already happened or to one which will happen? Then there are some more technical questions such as where exactly (time-code locations) the cue should start and stop, will it be a soft in/out, a hard in/out or do you want the ending/beginning looped for a period of time so you can decide during the final mix where you start the fade in/out? Any music cues I (the composer) suggest will be justified in terms of these same questions.
Directors will often have a much better idea of what they don't want than of what they do want and a composer always has to bare in mind that a director does not (and should not!) know exactly what they want. What I do expect of the director is that they have a highly detailed knowledge/vision of what they want their audience to be feeling, of all the characters and of all their motivations and of all the background story details which are not explicitly mentioned in the script. In my experience, directors who have some specific musical knowledge are often the most difficult to work with as they will sometimes try to use musical terminology and not fully appreciating the subtle implications/ambiguity of that terminology, end up inadvertently misleading the composer!
While we all have egos, when working professionally the composer's ego is usually at the very bottom of a long list of the director's priorities and composers need to accept this reality and get over it or find another line of work! Obviously though I would expect the director to have at least some respect for my opinions, otherwise why did they hire me but in most situations others' opinions carry more weight (for example: The editor, the sound designer, the re-recording mixer and always of course, the director and producer).
I hope some of this is useful.
G
