Hello! I'm a songwriter to and what do is: I just pick up my guitar and play until I have this 'cool' riff/chord progression or anything else that sounds good to your ears. Of course, you gotta have some experience with playing different types of songs. Knowing all sorts of chords are committed as well.
After the discovery of your new chord progression you just keep playing the pattern. It's helpfull to close your eyes and imagine something that fits into the song. It could be anything. Your girlfriend, your mother, a landscape at sunset or even the office you work in. Let your imagination do the work.
Get some paper now. Write down anything that comes up in your mind. Of course, it must fit into the thing you imagened.
Put those lyrics into your song. To get some nice music when you talk about vocals, just listen to a lot of songs.
Last but not least, you have to get a catchy riff or hook in it. Keep that part simple, people must remember it. Be honest, which part do you think of with the song Neven Nation Army? I think of the guitar riff. Get a catchy riff.
I hope this was helpfull. Good luck!