Well, i am not call myself as a "songwriter" yet: i just put my hands into the raw clay, moving my fingers and see what's happen.
But...
...sometimes i have just a phrase that turn around in my brain (words and music) and some other times i write the whole song (at least the fisrt "glance") in 2-3 hours.
It happened with my last song i wrote: i lestened two girls (around 14-15 years old) talking, on a train. I couldn't not to don't listen, because they talked loud and i was near them. They talked about their lives and the boys. I smiled on myself, thinking about my teenage, and in my brain i heard a voice, singing: "You, young woman". When i went home, i wrote the phrase and half a song came into my mind. The other half, i wrote it in 2 hours, both words and music.
But usually the whole process costs me longer. Very long time.