He probably used a vacuum press: the dash is inserted in a heavy-gauge plastic bag, with the veneer in place, and a pump takes out the air, creating significant pressure for the veneer to set onto the dash (using contact cement). This way, the curvature shape of the dash is matched by the very thin veneer. Afterwards, coats of lacquer that make the veneer take on the appearance of solid wood. So, James, I guess there was an airbag in the equation for some time at least!
It does look awful in my personal opinion ...