Wells in castles in England could be 100 feet deep, some could go deeper: at Clarendon palace in 1482, payments were made for a rope, probably to draw water, of 24 fathoms, which is roughly 140ft - giving a sense of how deep that well went.

Many well cut into bedrock at a certain level, which means that the main concern in terms of maintaining a well was in its upper levels. Some wells were constructed in these upper levels by constructing masonry walls with neatly dressed facing stones, giving the walls of the well a smooth, circular profile.

The builders of poorer wells might not have access to stone or mortar, so superimposed barrels with the tops and bottoms cut out, to create a timber lining of sorts.

I don’t know of any sources which discuss the construction of wells per se; some documents tell us that, for example in England, that Robert de Westmallyng was paid 20 pence per foot for digging and constructing a masonry lining for a well at Sheppey, England, in 1365. For the castle at Queensborough, Robert Weldyker [‘well-digger’] was paid £10 for 60 weeks’ work to dig a new well, suggesting it was a significant bit of work.

Sources for three dated references: Salzman, Building in England Down to 1540: A Documentary History: https://archive.org/details/buildinginenglan0000salz.