Different field (product design) but same sort of issue as the op - well I'm assuming the op is not glossing over any lack of skills/talent etc getting in the way - would be nice to see the work you're producing so we can give honest feedback etc.
My ideas don't always develop in a 'step by step' approach required by 90% of educational courses (typically my uni apparently changed this after my year left lol).
What generally happens with me after the brainstorming stage is I have a couple of initial ideas and then the next thing I'm doing is seeing the merits from x and y designs and come up with a design that is in course terms about 10 steps further on as I've kind of thought about it in my head rather than on paper.
The thing that I notice more now is that I just randomly put down ideas on paper, lots of random little sketches which are off shoots from the 'brief', I would guess this is likely what your courses are looking for.
I'll give you an example (remember I'm not graphic I'm product design but the principles are the same really) of how I work(ed) based around my entry to the
wolf soda comp (it's post number 2). Remember this doesn't always work, sometimes the idea is just there.
1) analyse the brief, take out keywords, look at definitions etc
2-4) these all happen at roughly the same time:
brainstorming around those keywords, look at offshoots which might directly relate but may help later on
highlight important elements of the brainstorming
written and sketched initial idea
5) break down the initial ideas, looking for parts which are good and bad - in my case two elements stood out - werewolf, silver bullet (it's explained on the entry) which led to the idea of a bullet
6) look into 'bullet' designs to help with developing the idea - measurements, shapes, materials (in my case this was defined by silver)
7-8) in my case model the idea in cad and evolve the idea to a functional product, this is where I often skip steps because I kind of fix issues on the fly, the tutors usually wanted to see the 'development process'...
9) chose the materials
10) sort out the 'presentation' layouts - I do a fair few quick sketches go for this stage
11) do the renders for presentation
12) post processing - adding text, finishing touches that sort of thing.
edit: exactly what type of course are you applying for?