In our collection, I have just catalogued an example which illustrates the process beautifully.
The piece is a 'slop' bowl in a European context, or a rice bowl in an Oriental. The Chinese original was produced during the reign of Kanxi, in the early 18th century; the European decoration was almost certainly done in Holland in the 1720-40 period.
It has the appearance and colours on a Japanese Imari piece, complete with chrysanthemum head mons- an effect the European painter was striving for.
But under the colours, you will see the original design: a series of leaves and plants in deep underglaze blue.
The peach colored panels are very unusual. They have a scraffito, or scratched in design of scrolling leaves, which is further enhanced with gilt lines.
The reason we can tell the original as opposed to the later decoration is the glaze: the original is the blue beneath the glaze, while all the European decoration is on top of the glaze. This decoration has unfortunately not bonded with the glaze too well, and in the above pic you can see the onglaze blue just beginning to flake off.
In the above photo, the blue has completely peeled off the glaze, leaving the underglaze blue leaf visible.
The best book on the subject is a recent publication by Helen Espir, "European decoration on Oriental porcelain 1700-1830".
Interestingly, the peach scraffito ground with gilt detailing doesn't appear in the many illustrated examples.