I usually write a text, or a poem, about something that has touched me.
Then I try to read the text, and the music seems to get out of the words alone. I write it down then, and I tweak the melody a bit to make it sound a little more elaborate and nicer (I put arpeggios or chromatism that usually don't come up in a song with that way of working).
I try to find a chord progression that will fit the melody after all this. And what's cool is that you can fit lots of progressions to the same melody, so my song is pretty much finished by then, since I keep a progression for the verse, and one for every part of the song. I might also tweak the rythm, or harmonize the line, to sound unusual or fresh...
I've written kids song that are being published in France, and I'd say that most of them came up this way. Creation is an amazing thing, since it seems to get out of nowhere.