There is now a distinction between the architect, the person who draws up the plans, and the builder, the one who decides how to put the plans into effect, hires the workers, assembles the materials, and supervises the project. In the Middle Ages the same people did both.
However, once a project was properly underway, the architect/master builder might hand it off to a second in command while he went off on a new project. Although we almost never know their names now, the best seem certainly to have been well known in their own period and were highly sought after and highly paid.
One of the first steps was to decide how big a building was going to be. One could make what was essentially the same church in different sizes, by having the basic unit of measure be different lengths. That is, if it was decided that a church was going to be 10 "units" wide, then one could make it bigger or smaller by lengthening or shortening the basic unit.
For example, the abbey church of Cluny, which was the biggest church in Christendom from the early twelfth through fifteenth centuries, was reproduced in miniature a short time later by the abbey church of Paray-le-Monial, shown here. (Miniature is probably a misnomer, as the church is still big, though not a contender for biggest church in Christendom.)
Paray is actually quite useful for knowing what Cluny looked like, because most of that church was dismantled by Napoleon to build his stud-stables. All we have left of Cluny is a few walls, what archaeology reveals, and drawings made before its destruction.
For a long time historians of architecture tried to figure out how long was the "medieval meter,"in the assumption that the "basic unit" for all church building must have been some sensible multiple of the "medieval meter," like 1.5, or 3, or something. All they had to do, they thought, was find some length (87 cm?) that, when multiplied by a series of sensible numbers, yielded the length of all churches' basic units. But they never found it because, in fact, there was no medieval meter. Medieval writers spoke of feet and inches and yards as we do, but there was no universal standard against which these were compared, and for most purposes it didn't matter. For the architect, the "basic unit" was laid out on site at what looked like a good length. Everything was measured against it. It didn't have to be a sensible multiple of anything.
Medieval architects, without knowing calculus or having access to CAD (computer-assisted drawing), and working with Roman numerals, were amazingly good. They built towers, walls, and arches that have stood up just fine for eight centuries or more. They did sometimes experiment beyond the limits of what is actually possible, such as in the case of Notre Dame of Paris, the first really big Gothic church, where the walls showed signs of buckling from the strain after about fifty years, leading to the invention and addition of flying buttresses. At Beauvais, the architects attempted to build the nave higher than any other church, some 130 feet high, but it kept falling down; no one has been able to equal that height without steel-frame architecture. (At Beauvais, they eventually gave up.)
After the destruction of the French Revolution, nineteenth-century architects tried to reconstruct what medieval buildings "must" have looked like. The leader here was Viollet le Duc, who made new, rather insipid heads for the kings and queens on the facade of Notre Dame and added the grotesque gargoyles (sorry, they're not medieval).