As several have already said, there are a lot of different ways to skin a cat. About 90% of my songs start with a "Hook" - the catchy phrase or primary subject of the song which becomes part of the chorus and which I also usually put in the title. Once I've established the hook or focal point, all the verses and the story of the song supports the hook. I try to find words that rhyme with the primary accent word of the hook. Its during this phase I usually work out the rhyming scheme, such as ABAB (end of A lines rhyme, end of B lines rhyme) or maybe AABB, ACBC, etc. I usually shoot for a different rhyme scheme for the verses and chorus, but that's not set in stone. By the time I get a couple verses written I begin to get a feel for the meter and rhythm of the song and try to ensure the prosody is correct. I'll sometimes switch to all minor chords for a sad song, etc. Sometimes I find a phrase in a verse I've written is stronger than my hook line and the new phrase becomes the hook and the old hook becomes part of a verse. Its more of a craft rather than an art.
I keep a "hook book" in which I jot down phrases I hear, things that I overhear people say, comments or headlines on the internet or local paper - anything or subject I think would make an interesting song later. I usually drag out the book when I'm in a "writing mood" to see if there is anything that jumps out at me. About 10% of the time after coming up with an interesting little chord progression or lick, I find a hook in my book that seems to fit the mood of the guitar riff and I start that way. - Its all good. I should also mention that most of my songs would be considered country/Americana in which the story is the primary objective rather than rock-style songs in which the beat and rhythm are considered more important than the lyrics - I'm guessing most rock songs begin with the music instead of the lyrics.
I always worked a lot of crosswords, sudokus and other puzzles and have found that I may not finish a puzzle I started in the morning, but for some reason the answers come easy in the evening, and vice-versa. I've experimented somewhat and wrote songs at different times of the day as my brain seems to work differently at different times. I tend to favor the songs I've written in the morning but that may be because I'm basically a morning person. My favorite writing method is to be out on the road driving early in the morning with the radio turned off and my mind making up songs to keep my brain busy.
Having hung out with some NSAI songwriters for a couple years, I'm alsways amazed at the variety of methods used by different folks.
DE