I come from a songwriting background and therefore, I tend to start with the main melody as well as the colour/vibe/mood I want to create. I will jot this down on whatever piece of paper I can find (I'm also a fiction writer and therefore always carry a notebook with me, which is a habit I highly recommend).
Afterwards, I will transfer it to notation paper and develop the idea. I sometimes create full stories where each instrument represents one character and each of them has its own story arc, and I then try to express this through music instead of words.
Once I have the main idea/theme and the direction/mood worked out, I will input it into Finale (I'm still using Finale Songwriter but I plan to upgrade to Allegro).
To compose the other instrumental parts, I tend to work by groups of 4 or 6 bars and compose all the parts through for them, then I move to the next block.