To me, if a thought process isn't innate, then I must consciously traverse it, step-wise. I suppose processes that I haven't been rigorously taught may consist of a set of steps which are only somewhat dependent on order, and I stumble my way through fulfilling requirements as necessary. Either way, I must consciously make my way from one part of a sequence to another.
This involves calling up the next step, which can be fast if the steps have been rigorously learned, or slower if I must analyze the process and determine (perhaps through logic) what the next step should be. At the same time I must temporarily save any data pertinent to the current stage of the entire process, to be utilized either immediately or further down the "processing pipeline."
I believe that makes a decent generalization of conscious thought processes for me, and it probably applies to most people. The act of performing this process in itself is a conscious decision, which the mind's eye must also keep itself aware of. Otherwise, it could get distracted, and lose itself in some tangent during a step in a thought process and either hamper the efficiency of the process or never finish it altogether.. All of that can also waste considerable processing power ;)