there's four and twenty million ways to write songs. I'm sure everyone hear has a different "method." I just sit and start strumming (not really thinking about it), and if the chords all sound good, I start to sing (mostly non sequitur babble) and a vocal melody just creates itself, then I turn the gibberish into actual words. Sometimes my lyrics are personal. Sometimes they're random streams of thought and/or nonsensical. But as I said, everyone here will have different methods to writing music- that's just how I do it.

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what i do is i listen to people [mostly my firends] talk and write down anything i think might be good in a song i havent worked out yet how to put music to it yet tho lol.....

I write the lyrics, and if theyre about depressing things like break-ups etc, then i sing them in a sad way, and vice verca. then i find the chords that most fir the tune im singing and add any riffs or solos after. its not as if im ever going to be in the charts or out, so if i like it, it'll do me :D
good luck

Like Def said, there's plenty of ways. What happens for me most often than not is I start with a riff. Then I try to build form there until I have almost a complete song. If it's a strong riff the rest seems to come together pretty well...I can almost hear where it's going next. The feel of the songs helps me dictate the lyrics if I have any...sometimes I leave it to the singer. On rare occasions lyrics come to me before the song but I find I have alot more trouble writing that way.
If I start a song and I hit a snag where it doesn't seem to lead anywhere I leave it alone almost immediately. Good songs aren't forced...frustration leads to compromises and you end up with a song you're not happy with.
Strumming is a good way to start to build your base...record that if you can. You have your basic chords and you know where the song is going. Then listen back to it (over and over if you have to) to see if any riffs pop into your head that you like.
A basic song structure would go something like this: Intro, verse, verse, chorus then repeat.
Hope that helps!!

i write pretty much everything on guitar pro, its great for experimenting with different drum beats and basslines and once you've written all the sections of the song you can mess about trying different song structures. you can get a free demo at http://www.guitar-pro.com

I like to come up with a concept. Something that moves me. I'll then come up with some lyrics and then match some music to fit the mood. However, other times I come up with some great music that reminds of something that moves me and sort of massage the lyrics into place however I can. I'd say it goes 50 / 50. But it's always involving a personal connection with something.