Everyone has their own way of writing and arranging music, so most things are entirely dependent on what helps you to be at your best creatively. Personally I work my best after writing out a chord chart and the structure of the track on manuscript paper or Sibelius, and then I like to come up with ideas on my violin or piano which I then start to score down.
Most of the time producers send me group stems of the track so I am able to isolate individual parts and focus on key moments that I can lock into - be it something that is rhythmical, lyrical or even a small motif that stands out to me. I also listen for prominent moments and create ways to build up to them.
Once I have figured out moments in the track I want to highlight or embellish with strings, I then look for the gaps that enable me to be creative and write my own interpretation. A few of my favourite arrangers such as; Nelson Riddle, Simon Hale, Larry Gold, Miguel Atwood-Ferguson, all have their own creative individuality allowing them to do their own thing.
As there are many incredible synth strings out there my big aim is to record and write something that strays away sonically from those sounds - something only live strings can create. To do that I think about characterising the piece with phrasing, bowing, extended techniques and dynamics etc.
These things are also important to think about when you want to differentiate roles between supporting a melodic line (singer or instrumentalist) or the strings being the main focus.
Most importantly the key is keeping enough space for the rest of the instrumentation by choosing the right moments to place the strings for the best impact on the track.