I find that lyrics are often a very important part of a song. They may not be absolutely crucial, but they can elevate a decent song to an excellent one by presenting the listener with images or phrases that strike the mind and the heart. A band who do this excellently is Jawbreaker; Blake Schwarzenbach's lyrics are frequently peppered with images and strong emotion recall.
My own personal method involves a few simple things that I find aid my lyric writing exponentially.
Write All The Time.
This is key; just write, and write, and write. Any time you feel like it, write something. I find that doing this late at night is especially productive, as your subconscious is more active in the twilight hours, thus potentially creating more interesting imagery and metaphor. This will generate a large body of work which you can pare down into more concise pieces, that is to say, your songs.
Don't Worry About Rhyming.
Really, you shouldn't make finding a rhyme scheme the be-all and end-all of writing. If you can do so and still convey the images and emotion in the lyrics, then great. But don't force your lyrics into a rhyming pattern for the sake of it. Look at these great Jawbreaker lyrics from the song 'Ache':
"I believe in desperate acts.
The kind that make me look stupid.
(Look like a fool)
Just keep reinventing myself.
It's move or die.
(I change my form)
These days the people I love
are spread so far apart."
Schwarzenbach's lyrics do not neatly ascribe to a rhyme pattern, yet retain an undeniable emotional punch and clarity.
I hope that this lesson is useful, I speak only from personal experience and wish to pass on techniques that I find effective. I hope that they are of use to you.