The previous outlined steps for the most part apply, here, with the exception of workmanship quality, which won't be as critical. If the lumber is to be covered with lath and plaster or stone it can be handled in a couple of ways. If the brackets are being placed during the construction of a new home, it might be easier to use a conventional lath and plaster. It would be best placed over the house lath, scratch, and brown coats with the color coat to tie it all together.
The other substrate for plaster or stone would be a cementious backer board attached as shown.
Bay Windows and Corner Windows
The installation of bay window and corner window boxes is very similar to a regular window except each section requires a set of brackets. It takes a little more skill to get the corners to fit. The facias need to cantilever more to make the adjoining corners. The gap can be covered with a top piece, or a bottom can be placed in it.