Songwriting
is a nice way to share private thoughts in way that hopefully gets other people thinking about themselves and not you.
About half the time, I've got a clear idea of what I'd like to communicate in a given song. Then it's just a matter of picking my spots, when to be specific vs. keeping it general. However, I've also found that what's literal for one person's experience will often serve quite nicely symbolically to someone else.
The rest of the time, I'll just let the music inform me as to what the lyrics should be. I have no doubt that whenever I think I'm just "telling a story", my own personal experience is written all over it.
As for the actual musical part of songwriting, I don't usually have any specific sound (or even genre) in mind. I just fiddle around on the guitar (or drums or keyboard) for awhile until I hit on something interesting. I'll play with the tempo a little until it sounds right, then it's just a matter of getting a very rudimentary recording of it that I can accompany to begin layering it with chords/a drum beat, or whatever.
Of course, there are still times when I set out to specifically create something with the feel of an artist or song that I love (a pretty full list that ranges from the Beatles/Zombies/Animals/CCR through to 80's bands like the Police, and up to 90's bands like Cake, Radiohead, etc..). That said, whenever I do set out with a deliberate sound in my head, the end result invariably sounds nothing like my original intent (which is fine with me).