Good question.
Honestly, most of my writing has been from necessity. I’ll look at the set list and think “I need a ballad”, or “I need tempo”, maybe replace a cover or cook up a fresh alternative to an existing bit.
I”m motivated mostly by what I perceive as failure in the existing material to serve the strengths and habituation responses of bandmates and audience.
It’s work basically.

Point being, I don’t get to “how to write” until I’ve gotten past “why”.
If that’s where you’re at with your block, don’t beat yourself up, not everybody’s a songwriter motivated entirely by a burning desire to write.
I know quite a few folks who just churn stuff out and it’s all mostly great, that’s not me.
In any case we all need reasons to write, and some folks get their motivation from internal pressure, some from external. .

Assuming sufficient motivation, anything goes.
The majority of my instrumental tunes began with lyrics; a phrase or a name inspired an internally sung melody and developed from there.
But whatever’s going on for me with melody writing, it’s ALWAYS sung, it has to sing, I have to really like where the melody sits with the harmony to commit.
That might mean “hearing F#”, singing it, and then deciding if the harmonic perspective is F# D E A, or G# E F# B or E C D G.
Is the melody a chord tone? what degree? etc.
You’d think most of those decisions would be obvious, but I spend a lot of time nibbling around the edges of those assumptions just in case.

Some tunes start with a scheme or sequence, successive iterations of which suggest various resolutions, It’s Up to You was one of those.
The idea was “shortest possible melodic cell before change of direction” so two notes up, two notes down, until a phrase emerges.

The verse for Brother Mike didn’t just begin on paper, it was literally a topological transformation of a written list.
I got the idea from Mathieu, but basically I wrote pairs of chords, major above and minor below, extended the sequence until it looped, folded the paper beginning to end, then folded the bottom to the top, staggered the triad pairs and selected a section.
Was there an easier way to come up with A, E, C#-, G#-?
I should sure f’king hope so, but it wasn’t available to me that day, and it got the ball rolling so ok, I’ll take it. .

Ice Cream was written in response to Ray White being able to immediately sing anything I played even while I was playing it.
So I thought, ok, I’ll make some long slow ascending scalewise melody and repeat it at the octave, somewhere into the second 8va I’m sure to shake him!
Naturally he sang the whole thing straight up. .
The chords at the top were literally a joke, a musical joke, nerd stuff.
It’s D/G, E with A on top, E with A on bottom, D69

Get it? E triad with A in the soprano voice, E triad with A in the bass?!? LOLOLOLOLOLOLOLOLOLO… hahahahaha spit. .
Yeah, I “wrote” that.
So, the chords were a joke, the B section melody was a prank on the vocalist, and the blowing changes “A” were just a place to stretch and address a need in the set list for tempo. AS previously mentioned.

Bad Hair addressed what I saw as a need for a mid tempo Bo Diddley-ish triadic kind of 1st position romp to balance out the “too much space music” aspect of the set list.
Stuff like Bad Hair comes out as the negative space of a set list full of funk licks in 11/8 and altered harmony.
If it works, you write some more like that until all the E7#9 11/8 funk is purged from the repertoire, at which point you’re compelled to write some more composed thru prog fusion crap. Lather, rinse,

Hillbillies was a Bobby Vega bass lick, a train groove, and one galactic standard jamband Franklin’s rip, eventually collapsing into an altered chord to justify it’s very existence. Not exactly Lennon and McCartney, but if played with sufficient energy, it’s danceable.
It’s also a good example of collaboration, and an agreeable ensemble.
None of that stuff was belabored, it was all “I got a lick”, “Ok, how about this?” “Ok, and then!!” done.
The arrangement evolved, but the parts just kinda fell out as an expression of creative good will.
Not to discount the genius level work of any Bobby Vega bass playing, he obviously worked his ass off, but by the time you get to workshopping stuff, the individual musicians abilities are baked in. KVHW was not lacking for talent.

EEgads, I don’t remember that one, but odds are good it fit whatever template we’ve hinted at so far.

Satellite City was stone cold deliberate songwriting collaboration from top to bottom between Johnny, Leslie, and myself.
Obviously some bits leaned to one principal writer or another, but the basic idea was trusting each other to unselfishly start and finish a body of work.

The seeds for a couple of those tunes, Satellite City, and Variation, (at least,for sure) were Fender triple neck and quad neck 8 string tunings I had used on The Last Danger of Frost recording, and Orson was built on a 12/8 12 string and kalimba loop from that same record.
So in addition to collaboration, writing from lyrics, wringing out sequences, writing to fill negative space in existing list, inside musical jokes, challenging bandmates, and shamelessly borrowing from existing Grateful Dead songs, we can add recycling our own material to the “how to write” pile.

I’d be happy to discuss further, but for right now the answer to the “how to” question is the same answer as the old studio joke “how do you make a hit song?”
Any way you can.