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.

Musical beginnings

Although my music is not very inventive, it is intended to give praise to the wonderful God of Creation, and so I hope He doesn't mind too much.  In about seven (7) places in the book of Psalms in the Bible it does say we should "make a joyful noise", so I'm just following in the footsteps of those who went before.
Theoretically speaking, I am not musically proficient; for example, I can not "sight read" standard music notation, and this has meant that I do not (as a rule) play other people's music.  However, I have been playing the guitar for over 40 years, and so this has meant that I have developed my own form of notation, mostly just with chord diagrams carefully placed over my lyrics, and with other descriptive notes about special treatment for particular passages.
In my teenage years, I remember listening to my sister sing and play guitar in some of the folk-clubs in Adelaide, where I grew up. For my sixteenth or seventeenth birthday, I think, my sister gave me a book of guitar chords (2,400 of them), and I learned how to play a few simple chords like 'C', 'D', 'E', 'F', 'G', 'A-minor', 'B-minor' and 'E-minor'.  Talking to one of the guitarists at one of the folk-clubs where I had gone to watch my sister perform, I was shown how to play a simple lead-run of a few notes in the key of 'E' (probably E-minor), and my love of playing the guitar suddenly took a bright new turn.  It was about that time that I started playing in a band; a few mates and I used to get together in somebody's garage on a Saturday, and we would bash out our own renditions of popular songs, and also we would play some form of our own music - we developed the ability to 'jam' around.  A few years later when I was in the Air Force, and when I was not on duty, I would while away the hours twanging the strings on my guitar.  At various places where I was posted, I would usually find other like-minded souls (people with a desire to play music) and we would get together to play a couple of songs on a Saturday evening.  Gradually my guitar playing was beginning to improve, or at least, it was becoming to sound more the way I wanted it to.  I have no doubt that many people who listen to me play will think that what I play is rubbish, but then it is impossible to please everybody, and perhaps that explains why there are so many different styles of music.  Some people like it loud and heavy, other people prefer a more easy-listening form.  Some people like nothing but classical music, other people prefer jazz.