How can I build an insert on a desk that adjusts the height of a sewing machine?
My sister has a working surface for this purpose as well. Except there isn't a mechanical swivel to raise and lower it. 

There is simply a drop in the desk where the machine fits. Like a small cubby, lowered from the surface. If you were to search for "sewing desk" I'm sure this is what you'd see.

Then, when she isn't sewing, a piece of glass fits into a shallow rim around this hole to make the work surface completely flat. 

Consider this log at IKEA Hackers: 
http://www.ikeahackers.net/2012/07/melltorp-to-sewing-desk.html

A simple cut-out, except that the surface piece is removable.