From Furniture Designing and Draughting (1907), by Alvan Crocker Nye, we have this wonderful diagram on how to make a table.
The top row shows names of the common parts of a table.
The next two images show a number of ways of attaching the legs. The one on the left shows the frame both being doweled to the leg and using a mortise and tenon. The frame itself is connected with blocks which tongue into a groove in the frame. The drawing on the right shows a cleat screwed to the top, with a leg tenoned into the cleat.
Continuing down the drawing is a “section of a built-up top”. As a solid wood top is expensive and hard to come by, tops were often built up with a core and covered with a finish veneer to make it look like a piece of solid wood. A piece of cross veneer was placed between the core and finish veneer; this is a piece of veneer in which the grain runs perpendicularly to the core and finish veneer.
The bottom row shows various means of securing the top to the frame. The left shows a screw which is countersunk nearly halfway through the height of the frame. The middle illustrates a pocket hole screw. The drawing on the right shows the blocks which were previously illustrated up above.