Everyone has their own process, but a majority follows the same basic formula that is pretty much engrained in most of us either from a natural progression or formal training.
I'm taking an illustration i've done at work as an example. The fundemental process is a no brainer: Thumbs -> rough or polished work -> color roughs -> final
The current illustration i'm using as an example is for a development project years ago. The simple art direction was to take heroes and villains and put them in a Rockwell like thanksgiving pose. It wasn't hard to find reference as this particular painting from Norman Rockwell has been spoofed numerous times for comics.
I first started out with same basic roughs, trying to get what each character is doing or how to make the composition flow better. I find myself usually detailing up the roughs i really like, while others i tend to just jot down quick info to see if that composition worked. I even tried to see if the composition could work horizontally in a landscape. I found myself leaning towards the lower right design the most, and once it was approved, went in to detailing it more.
Some artists can skip the detailing stage and go straight into painting. I find myself needing the extra detail, otherwise i just get stuck painting. Once detailed, i normally go through a black and white value study (here is done slightly in pencil) and color roughs, exploring different pallettes.
Because the original art direction was "spoof much as possible," i didnt do too much color roughs and went straight into color. On the left panel, you will see me splashing in quick color just to get an idea of general/local color. The progression after that is just me working into the painting on a single layer - literally painting it up (I dont do this anymore, as i'm finding more often than naught that people always wants changes last minute. Now a days, I use quite a few layers to make my job easier in the long run). I start detailing and rendering like mad trying to get to the final look.
The final touches ( logos, text, etc...) are added after finish - and there you go! a finished illustration that suits the needs of the client and fulfilled art direction clearly. Overall, i enjoy this process because it's predictable and systematic - i can easily gauge the time required to do a finished piece and how polished it can be. Rarely do i jump in and do an illustration straight up; more times i find that way leads me to go back and do some arduos fixes.
anyways, this piece is now a large poster hanging in our office :)