I tend to get most inspired when I listen to, or passively hear something that inspires me (duh). So what I've started doing is hunting down where that bit of music I heard on an advert, or film or [insert generic media here] is originally sourced from and load it up in my daw.
I'll then deconstruct the harmonies, rhythm, melody e.t.c. (say if it's a pretty complex piano/orchestral melody/piece) so I can 'see' it's innards in front of me.
I'll then do a lot of thinking and experimenting in regard to the underlying motifs I've uncovered and do my best to develop them and take them in my own direction. When re-creating it I'll tend to try and mimic the original sound as closely as possible and then when I'm developing it I'll experiment with different timbres/rhythms e.t.c. I think will compliment the intended emotional message. To extend this, I also think it's important to experiment with different interval relationships within the melody and harmonies (which often take the vibe in a drastically new direction)
Wether I use an accompanying drum track is dependent on whether I think the piece sounds like it needs it at that point, which involves trying it out and comparing it to what I think it's trying to 'say' with what a given drum track does to it. If it doesn't work I'll leave off the drums until it's more defined as an idea. The same goes for specific timbres, textures, intervals, rhythms e.t.c. All the while I'm basically trying stuff and assessing wether it's adding to the collection of ideas in a coherent manner, or confusing the message.
That's the point of this step. It's analogous to a sculptor hacking bits of clay out of a block and smushing bits around in a mediation between creative accidents and careful deconstruction of what's actually happening in that relationship between the artist and the piece, in order to form an over all concept.
I restrict myself through this process by making myself not worry too much about complex sound design, the fidelity of engineering and all the other delicate, detailed technical processes because I think this massively hinders creative mindfulness.
I'll generally try to do this over 1 or 2 sessions while the original inspiration is still fresh. But once I've got to a point where I can think "yeah this has a strong identity" I'll save it, bounce out what I've done and spend a few days listening to it on and off (not too much because there's a danger of getting sick of it). While I'm doing this I'll think about how all the elements interact, focus down critically on certain things that are sticking out in a good or bad way and develop them further mentally. The more I listen to this 'proof of concept' piece the more I'll hear it 'better' in my mind until there's a definite and solid set of things I want to do and directions I want to take it. Here I'll be thinking a lot more about sound design, fidelity, groove and all the other semi fine details.
I'll then open the project. Copy out 1 element I want to revise at a time and work on developing that piece alone, out of the context of the song. This is what I'd class as the 'sound design' sessions where I'm not thinking about the song, I know where it wants to go, I know what i want things to sound like, and I'm working on those sounds alone, giving them justice without worrying about the bigger picture. These sessions will last a while where I'll do my best to get the different elements 'finished' and then pull them back into the track and put them back in place. I'll keep doing this till I've got to a second 'plateau' and I'll do the same as I did before. Bounce it out, listen to it for a while, think, imagine and develop.
Eventually it comes down to tweaking the little bits, adding little fx and the more subtle little atmospheric elements that gives it a fuller and more finished feeling. The problem with me is I seldom get to a 'finished' point with a tune because through the whole revision/sound design process I'll get inspired by something else and drop the current project which inevitably ends up on my SC as some unfinished half track 'concept'

But this is my general workflow, which I've got to man up and stick to much more than I do...