I know that legions were as much an engineering force as they were a military force, but what did that actually look like on a day to day basis? When building a road to press into distant territory, how many men were needed, and how much time? What tools and resources were needed? How many men with actual engineering education were needed in comparison to the men doing the physical labor? What is the most important thing to understand about legion engineering?
There was a praefectus fabrum (a chief of the builders) in the legion, but we have no idea how he was chosen, what his qualifications were, if any, and how exactly he operated. If he had qualifications, we have no idea how he came to enjoy them. More on that here.
That means we do not know very much about the meat of your question. The day-to-day of the engineering is very opaque. Every soldier could use a shovel, a hammer and nails, and could move dirt or rocks from point A to point B. With somebody at the top with the know-how, the actual labor of building a road is not too complicated--it's just a lot of heavy lifting. We know the legions had engineers and surveyors, and they had structures built-in to issue commands from the top level down to the rank and file.