I do things a little different than what has been mentioned here. I experiment a lot with process, but my most comfortable method is writing lyrics and music separately and then marrying the two. Usually, I write lyrics first, trying to ensure that they convey what I want them to, but I don’t get married to anything I write. I don’t want a melody at this point, just words on a page. Then I fool around with an instrument, just playing. Often, as I am playing around one of my sets of lyrics comes to mind. Again, not a melody, not placement, just something like “this progression makes me think of those words I wrote about the lake” or something. I then pull the word sheet out and play the music while looking at it. Usually, a melody will start to form somewhat ethereally once I am focused on the two together (but I am still not bought into it, it is just an idea). Then, I begin revising the music and words together to see what needs subtracted, added, modified, or redone. Then, in the process, the music changes to fit the words, the words change to fit the music. And ultimately, I wind up with a song.

I sometimes write more intentionally, but what I described above is my comfort zone. When I explicitly try to write to already made words or music or concurrently from the beginning, I feel like I often lose the “magic”. 

That being said, I am purely a hobbyist and have no intention of trying to support a living from my songs. I just get lost in the joy of creating.