I find that songwriting goes in waves. If I set aside the time consistently, and allow myself to be in the songwriting headspace, without any pre-conceived ideas about what might come out of it, the ideas start coming. It's like exercising a muscle, or stretching. The more consistently you do it, the stronger and more flexible you get. And what starts to happen is that ideas start coming all the time, not just when I've consciously sat down to work on writing.

On the other hand, when I let other things get in the way and DON'T make the space for it, the ideas stop coming, or if they come they are more feeble and it feels like work to bring them out.

As for the music/lyrics question, I have had it happen in all different ways -- music first, lyrics first, a snatch of music and lyrics together. I tend to lean towards lyrics first, but some of the songs I am proudest of are ones where I started with a line of music and words together.

In my opinion, there is no one way that works for everyone-- part of your task as a songwriter is to find what works for YOU, and do that. Other people can give you ideas about the process, inspire you with their methods or creations, give constructive criticism on songs, etc. But you are the only one who can find the techniques that will work for you.