I tend to write the music and the lyric simultaniously.
When I get a couple of cords and a sentence I like, I have a good starting point for letting the song evolve. I am not wery productive though, only 1-3 song a year, but I enjoy the process.
When I play in a band (shared songwriting) I usually have the complete musical piece finsihed first (or at least a complete verse or chorus), and I listen to I't a extencively. Eventually some nice vocal melodies will become apparent. Try fitting different lyrical structures to the music and so on (different sounds etc.).
I do write down sentences I find amusing or elequent down and occationally try to fit them into a song.
Reading decent litterature also helps improve the writing (both as an inspiration and to the craft of writing).