I never sit down and say, "Right, today I'm going to write a song". I've always found it important to wait for inspiration to find me, rather than chasing after something that isn't there.
I might be washing the dishes, walking round a supermarket, mowing the lawn or lifting weights, at some point an idea will start to form. Most often it's a combination of lyric and melody, maybe a rhyming couplet with a tune that naturally gels with it. It's only at this point that I will pick up my guitar and start to to flesh the song out. I will then generally write the song in one sitting, if I'm struggling to generate enough ideas to finish it then it usually gets ditched and I move on to the next idea.
The next step, for me, is quality control. I write the lyrics in my notebook (I never notate the melody) and leave the song for a week or two. If, when I return to it, the melody bursts back into my mind and I can remember exactly how the song is supposed to sound then it's a good song and worth keeping. If I look at the lyrics with a furrowed brow and can't recall the tune then it must have been a load of rubbish and it gets thrown on the scrapheap.
I think one of the most important aspects of writing is to have the courage to dispose of ideas that aren't working, they clog up your mind and can prevent you from exploring new avenues.