Currently I just mess about with bits of notes in no particular order to find something that sounds good then when I do find a little lick that sounds good I work out what scale they are in and then work around it from there. At the moment i'm messing around alot to try and sweep pick with some efficiency so I can add that into a solo.

As far as chord progressions are concerned generally I will just mess around with open chords, bar chords and power chords until such a point I develop a good sounding rhythm section - or at least something that sounds good to me. Everything with me is unfortunately a jumbled mess at the moment as i've only been playing just over a year and still learning (saying that someone once told me it doesn't matter how long you've been playing your always learning)

My muse tends to be boredom coupled with hearing a catchy riff in a song or in some theme music on a game or tv show and that makes me start out from there

If you are driving your car, DRIVING over a bridge, you can hear a kind of rhythm, the noise made by your car inspiring you? I did, and it was a really nice song. At home I remembered still a few things. So what if the "muse" hits you while driving? Do you register the basics on a cell phone or do you have always a "recording device" on the passenger's seat? Dictaphone, a zoom H4...
Or does the melody stays in your brains. It is really "dangerous"to continue listening to music in your car, your song shall be influenced by other songs.

- Zurf

For me, it is rare for the 99% part to happen within 20 minutes.  Usually, it takes much longer - but the initial ideas (1%) always happen very suddenly.  I believe a very important part of being creative is to be open and sensitive to ideas - however, without some diligence and real effort these flashes of brilliance are gone and quickly forgotten.

In New Orleans, the nine Muses are all honored with street names in the old Uptown neighborhood.  Just past Lee Circle as you head 'up' St. Charles Avenue you will see the streets named after all the Muses.  However, Urania St. is no longer there - I believe it was obliterated by the construction of a modern multi-lane elevated highway.

There were three original Muses: Aoidē ("song" or "voice"), Meletē ("practice" or "occasion"), and Mnēmē ("memory"). Together, these three form the complete picture of the preconditions of poetic art in cult practice.
In Delphi three Muses were worshiped as well, but with other names: Nētē, Mesē, and Hypatē, which are the names of the three chords of the ancient musical instrument, the lyre.

Isn't this an amazing story? See this:
The canonical nine Muses, with their fields of patronage, as established "since the Renaissance", are:
* Calliope (the 'beautiful of speech'): chief of the muses and muse of epic or heroic poetry
* Clio (the 'glorious one'): muse of history
* Erato (the 'amorous one'): muse of love or erotic poetry, lyrics, and marriage songs
* Euterpe (the 'well-pleasing'): muse of music and lyric poetry
* Melpomene (the 'chanting one'): muse of tragedy
* Polyhymnia (the '[singer] of many hymns'): muse of sacred song, oratory, lyric, singing and rhetoric
* Terpsichore (the '[one who] delights in dance'): muse of choral song and dance
* Thalia (the 'blossoming one'): muse of comedy and bucolic poetry
* Urania (the 'celestial one'): muse of astronomy

So all these NINE muses with their specific task. They are HELPING AND INSPIRING YOU to create a beautiful song. There are only nine so it is IMPOSSIBLE that they inspire every song writer.
Where do you get inspiration? In love, nature, protest in fact even a mosquito can be subject for songs. MY THEORY + IF IT TAKES LONGER THAN 20 MINUTES YOUR SONG WON'T BE GOOD.
In my case, I have the "car crash" muse, inspiring me to write down what I have in mind.

HOW DO YOU SEE WRITING A SONG?