I'm not sure they were built all that well. There were quite a few collapses and failures along the way. Certainly they were not built to the quality of todays buildings, but they were built to last, I'd give them that.

Castles are almost easy design wise, theyre so big and massive and simplistic in many ways that they didnt pose that many problems (relatively). Although towers were still prone to collapse.

Cathedrals are another story.

Cologne Cathedral was commenced around 1250, building ceased, uncompleted, in 1473 (200 years later!) and wasnt finished until 1880. That, by modern standards, is not a successful build.

Salisbury Cathedral was built with such an enthusiastically large spire that only periodic upgrades to its structure prevented the whole thing collapsing. Christopher Wren himself held secured the most recent strength upgrades.

Malmsbury Abbey suffered two separate collapses of its tower structures, mostly demolishing the building each time.

The people who built them were mostly Master Masons, stone workers who had worked with other stone workers enough to be confident enough to take such a job on. They would have learned things when they were an apprentice from a earlier Master Mason. There were also Masons Guilds as well, where information and knowledge could be disseminated.

These people and their institutions were crude analogs of the same things we have today. They would have been far more 'amateur' than today in the way things were run, organised and controlled. What wasnt amateur was what they built.

Engineering and architecture were still in their formative years. As a result there are numerous failures amongst the successes. What is not clear is how much 'political' pressure was brought to bear (Our steeple must be taller than Their steeple) affecting design decisions.

Modern professional style architects didnt come along until a bit later. Although like many of these things theres no formal start/end dates for such advances.

The Master Masons were often designing and building along the very bleeding edge of engineering capacity at the time, sometimes beyond. Most of the knowledge was informally trained from Master to Apprentice. What we see today is their successes, but often the successes that lasted long enough to be fixed up by the next generation along.

The Romans and their magnificent buildings I dont know much about. Buildings like the Pantheon, which STILL has the largest unreinforced concrete dome in the world, are equally as impressive as anythign built in medieval times.