I usually start with chord progressions, mostly on (acoustic) guitar, but sometimes on piano/keyboards. I jot down the chord sequences on paper and make a quick recording in my DAW (Samplitude). I can build up 50 or more ideas in that way before taking them any further.
When I am ready to start work on an "album", I then wade through the rough recordings and select about 10 to 12 to develop.
I then start working on the "full" recording of a song: I start by trying to find a drum loop that matches the timing of the song. I usually build up guitar, bass, drums and possibly keyboards to give the basic song structure. I may also record a "vocal" with ad libbed lyrics, just to get the melody.
At this stage (usually the first time I save the song in my DAW), I give the song a name: this can be inspired by the mood of the piece, plus I have notebooks with potential song titles that I peruse. I usually have some (often vague) idea of what the song will be about, but not set in stone.
It's only then that I start on the lyrics. Sometimes I go with my original concept, but often the lyrics take off in their own direction. Most recently, I have been spending a lot of time re-writing until I am really happy that what I have ...
I tend to work on multiple songs in parallel and can sometimes leave a song for several weeks at a time. As soon as I have all 10-12 songs completed (including getting review comments in this forum and using that to improve), I release through Cd Baby!
(Of course, there are many exceptions to the above
)