How do you write a song?

There are perhaps many ways to write a song.  Most often I start with some guitar music, usually just a simple chord progression, perhaps even just two chords that sound nice to me when they are played together. Next a few notes or a phrase of melody will come to me, usually implied or suggested by the chords I'm playing.  When I've played the chords enough times (probably too many times for those around me who also have to listen), then the lyrics will usually start to flow - mostly about what ever I've been thinking about lately.
Sometimes I might manage a verse or two and a chorus, and that might be all I'll have for some time, but then, as I begin to refine the song, playing and re-playing it to myself, and if I think it is fit to be played in public, then I will exert some mental effort to figure out some more words, and perhaps a bridge section sometimes.  Sometimes the words just flow, but sometimes there can be a mental block for a while.
As I mentioned in my initial post, I do not sight read, or write standard musical notation. One thing I have spent a very long time doing, is the repetition of various musical phrases that I like.  By varying the rhythm of what I play when I practise, I have gradually gained an appreciation of what musical ideas I like when I hear them. A set of chords played at some particular tempo can sound totally different when played faster, or more slowly, and the same chords played in 3/4, or 4/4, or 6/8 time, can take on a totally different feel, and will therefore help to suggest one form of melody over another, or will perhaps help to enhance a particular mood for the piece I'm working on.
On rare occasions I have written some words, or lyrics, first, and then set about trying to write a melody and the associated chords to harmonise with what I have.  Usually I find that process (i.e., words first, music second) the exception, rather than the norm.  But I have met other people for whom that is the way they will usually work.  I guess everyone is different.
The final production of a song might entail many other components, too.  For example, if you play in a band, then when you introduce the song to the other band members, you may find that your song will start to take on a life of its own.  Some people may have a very definite idea about how they want their song to sound, but I have found that other musicians can add much to the feel and interpretation of my songs, and usually the end result is better than what I had at the start.  Now that probably speaks volumes for the professional nature of the musicians with whom I play.
What ever you do, make sure that the process of writing your songs is fun.  If you are over-tired, or if your mind is somewhere else (i.e., you are distracted by other things), then it is probably time to take a break.  Return to the task of writing your song at some later date, when you can take the time to concentrate on what you are doing.  The result will usually be much better.  Also, don't be afraid of writing two songs and throwing one away.  That is to say, not everything I write will ever make it all the way to being a complete song that is worthy of being performed in public, but many of those incomplete pieces have served as stepping stones in the process of writing the pieces about which I am more pleased, and some of those find their way into the making of a finished song.