Everyone has what works for them, I've written lyrics first then put music to them. I've also wrote music and made up lyrics to go along, and I've also tried the both at the same time approach. For me, it depends on what I'm in the mood for, if I get lyrical inspiration I'll do that first, if I'm just noodling around on my bass, and I hear something I like, I'll work from there. It's really different for everybody.
Thats the way i usually do it , but always find myself second guess everything, then it turns into a mess. But the more i practice the more emotion i can get out of it.
I also have tried writing lyrics first but i usually get about halfway the loss all motovation because i hear no music.
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Little does the government suspect that it's funds are being rapidly drained through funding infinite free cardboard boxes to bored teenagers on an internet forum.
It varies from person to person. I've been known to do a little of each depending on when and what kind of inspiration hits me at the time. Sometimes the music just appears and I start writing it without a thought about lyrical content, other times I write the words, but no musical composition yet, and other times both seem to come together at once.

It all depends on which you can do and when your inspired. Sometimes you might be noodling around and accidently write a nice song, but have absolutely no words for it and other times you might think up a few lyrics in your head and not think of a solid musical outline for them. there is really no wrong way to go about writing songs, it's just which way you find easier.
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Cheers Sinister that was really helpful a Dime-point to you!

"Any problem you can't solve with a good guitar, is either, unsolvable or isn't a problem."
I do it both ways, depending on what Im doing.

I often play something until I find somethign I like and then hum over it and sing random stuff. Whatever I sing evolves into a song.
i write my riffs first, i just compose little pieces of future rock songs then worry about the lyrics later. i analyse the song and determine the sort of feel it has by getting second opinions and try to apply a lyrical theme, sometimes its like stuffing an elephant into a tiny box but i move the measures around, change the lyrics, whatever will make them work with the rhythm, i rarely write lyrical melodies, its usually Jerry Lee Lewis, Jimi Hendrix style singing