That, was 40 years ago, so the actual "process" is all but forgotten.
The case, is 3/4" square wood, with a groove cut in two sides, for the glass (sides, ends, and top, The bottom "rails" have the groove on only one side). The front and rear are assembled as you would a picture frame, the glass, permanently installed in the pre-cut grooves. The four, top, and end (short dimension) pieces, butt to the insides of the front, and rear , and the glass is inserted into the grooves during basic assembly. All joints are glued,The corners are secured with 1/4" dowels, through the front and rear pieces, into the end grain of the short pieces. small brads were driven through each rail, into the dowel at each corner of the front and rear "frames". The case assembly (with glass installed) was then sanded, stained, and finished with hand rubbed tung oil.
I have been lucky that the glass was never broken, as this method of assembly did not allow for replacement of the glass. Since then, all my cases have been routed to take the glass, which is held in place with quarter round, fastened outside the glass with small brads, in predrilled holes, to prevent splitting the quarter round. Two wood screws through the base board, into the bottom end rails hold the case to the base board, I also installed felt gaskets around the bottom to help seal out dust.