I almost always start on my DAW, but sometimes I'll have a melody or rhythm in my head and try to get it down.

I don't play any instruments well (see my other post on the topic) so often I'll just look at the piano roll and draw in something that I think will sound good. Yes, I will actually sit down with my mouse and click in notes in patterns that I'm familiar with. It sounds insane, but I've managed to get more comfortable with this over time. (I know some REALLY good musicians who enter all of their notes like this - one guy I know can crank out a 5-minute, almost fully-produced track with multiple sections and development and glitch and effects in a little over an hour with the mouse).

If I don't really know what to enter, I'll noodle around on my MIDI instruments for a while, almost always recording. Though I'm not really proficient in playing, I know enough to be able to do some basic scales, some chords (not at the same time). I'll record it in, clean it up in the piano roll. It's almost always useful to keep recording even if you're not really sure you are ready because something might turn out good and then you can keep it. If not, it's super easy to just toss it out and record something else.

One thing that I learned from doing a lot of compos is that it gets you into "write stuff mode" really quickly. You kind of get some visualization of what you might want to do as soon as you see a theme. I try not to think about it too hard anymore. I sit down and it's mouse to screen and hands to keys.

Now FINISHING tracks once they've been started? That's a whole other problem.