Actually, many of the one piece grips, including ivory, are just that, one piece. Colts and the Italians use mostly one piece grips on their SA revolvers. Many aftermarket one piece grips are three piece. The ones I make are three piece because it is much easier to makee the three pieces and fit them together. I use a Japanese pull saw, rasps, and sandpaper for tools. And a pencil. Sometimes a handplane to flatten the two halves to better meet the grip frame.
Another way to do it is to make two piece grips and hold them with a screw and escutcheon. I believe this is how Das Jaeger makes his beautiful grips.
I will be cutting a set of grips for one of my 1860s after the Holydays, maybe I will take some photos and post them.
Let your imagination go for grip material. If you want traditional, think fruit woods like cherry or apple, nut trees like wlanut and pecan make nice grips also. So does maple and ironwood. I favor stag, but ivory is a good choice if available. Exotic woods, zebrawood, rosewood, etc are also good choices. Depepnds on your taste and what you want to do. Ebony and other dense woods shift the weight back into your hand and will counterbalance a muzzle heavy revolver.
Have fun.