I usually either hear something in my head and try to work it out or I just faff around on guitar or bass until I play something I like the sound of. If it's something just for myself, I'd make a rough map of the song to a click track, flesh out the other parts. Often, at this stage, I'd have a line or two of vocals in my head too, a hook. I would do the full arrangement of the song to click, just with a rough guitar track and everything else in my head. Then I'd record drums - up until a couple of years ago i did this literally, playing and recording a full kit in the house but I wasn't playing drums frequently enough to stay at a standard I liked so I sold the kit and turned to midi - and build up from there. I always bounce down rough mixes as I go along and listen to them away from instruments, just see what I can come up with while listening and then try to figure out how to get close to what I envisage the song to be when I record it in the real world. It is all down to the work ethic though, much as I con myself otherwise. I really like the deadline of the composition competition, it forces you to do a bit of work which I'm hoping to take into the 50 or so songs I have in various stages of completion I started recording over the last eight or nine years - when I moved to a rural house with no neighbours so I could make as much noise as I liked. I find the ideas come easily, actually finishing something is the hard part but it's really is down to getting of your arse and grafting. I'm finding writing lyrics very hard at the moment. I want to have something of substance, tell a story, make a point, whatever - I used to write lyrics for a couple of my bands in my youth but it really doesn't come easy any more. Maybe it's an age thing.
With the band, generally, it starts with a riff. If I come up with something I'll record it into the phone and then come back and build from the drums up. I tend to leave the arrangements open, just record a verse, chorus and a couple of related bits and then let it be finished with the input of the entire band. Our singer writes the lyrics so I leave him to it.