Hi Jette,
I think it varies alot, like Rune wrote.
Also a composer might use different approaches depending on what he/she is writing.
For me there are 2 ways I normally go about the process, and I'm also, like you, interested in hearing others approach to composition.
I mainly write for classical ensembles of different sizes, and one of the methods I use is when getting an idea (melodically or rhytmically) I write them down using different notational programs on my computer and then "play" a little with them - some times the inspiration continues and more ideas come to life - some compatible some not... the ideas can range from a specific "voice"/instrument to a more general thematical and/or rhymical idea...
The process of writing the music down also varies - sometimes it's usefull to write a "piano-score" (without any specific instruments) and then when it's nearing completion you go about orchestrating it for the ensemble you're writing for and in this process other ideas might arise - sometimes it makes more sence to write for the ensemble from the first instance, for me this is mostly only valid in regards to a relatively small ensemble like a choir, wind quintet, string quartet aso. It's a bit of a task starting your initial composing by having a big score in front of you and then slowly start filling it out. Some might find this way more interesting, some might not.
It's not unlike paiting I guess - starting with a "skeleton drawing" of the subject you're painting then filling in some more nuances and finally putting on the final coat of paint (the orchestration part if you will). - Some might "just" "throw" pintcolours at a canvas or start painting the picture in "freehand" (the musical equivalent could be improvisation - which I'm sure Frederik can go on about for hours
). Again it varies.
But alot of the work in composing is knowing your medium, the musical theory behind and wanting to spend hours with a seeming small amount of "inspiration" to see what you might be able to derive from it - adapting themes, writing in a specific style aso aso. - Composition is rarely just a matter of writing the inspiration down (which can be hard enough) - it's what you do with the inspiration after you get it that, normally, shows your abillity as a composer (like your knowledge and abillity of orchestration or maybe your originality in adapting your material thematically and rhymically and more).
So composition is not unlike the cliché: 10% inspiration and 90% perspiration. So it's definately about talent, but there's much more than just getting a good idea!
This was the more classical approach to composition - composing/producing a cd is not unlike composing in general - it relies heavily on your knowledge of the possibilities in the medium (in this case the computer/audio production programs) - adding layers (drums, bass, guitars aso) and making them sound right, adjusting the tone qualities, cutoff filters (enhancing some part of the sound from the fundamental notes through the overtones).
Inspiration for all this might come spontaniously, or as an inspiration based on something you've seen or read (or felt!)... conveying emotions is one of the strongst elements to music - the universal understanding of emotions through music might change somewhat from continent to continent (depending on the historical/cultural heritage), but the general "feeling" is about the same everywhere.
I hope this did a little in helping you understand what it means to compose.
Looking forward to see more posts on this topic from others.
Thomas