Lots of different approaches, and I guess they all work. I probably do most of them. I sometimes write lyrics as I might write a poem, so with a rhythm rather than a tune. Sometimes I'll write a lyric to an existing tune; the last was a song for a historic project about union uprisings in the UK, put to the tune of downtown train (Down The Porter, by Rusts) - you'd never know, sometimes I'll just play chords and see what lyrical phrases and melodies come out of it. The key thing is write everything down, record every idea there and then, regardless of whether you're in the supermarket or speed-dating. The more material you have to play with, the better.
Mike