I don't write much but do have 2 pieces copyrighted. I follow a certain process. When an idea comes into my head I do almost nothing. I may sit down at the keyboard and fool around with it for a few minutes. I don't write anything down or record anything. I wait until the next day. If I can remember the melody, chord progression, etc I get started on finishing it. If I can't recall anything it wasn't worthwhile.
I have only written a handful of songs or so, and they have been pretty over thought.
But for what it is worth, I am a lyrics first guy.
It starts with an idea for a line or a rhyme within a theme that would make a song.
I then think up more ideas for lines/rhymes that would fit the theme and touch on aspects of it that could be addressed in the song.
If I have enough, I start putting structure to the song. This is tricky. Unusually want to have like 3 verses, and I might have 6 lines. Gotta find a way to connect the dots. What goes well in first verse, what goes well later. How to get the number of syllables to be close enough to fit.
If I manage to write acceptable lyrics, chord progress comes next. I usually have some idea of how I want the lyrics to be sung. I will try the part I feel most strongly about over different chords, untill I find one I like. Then I look up common chord progressions that would fit, and try them out. Sometimes the pieces fit together 🙂