Jennie, the way turquoise is (almost always) backed is simple- get
yourself some Devcon liquid steel (you can use brass or other, too).
On a flat benchtop lay down as much waxed paper as you need to spread
your pieces with a bit of space between. Mix the Devcon and spread it
out on the wax paper till it’s about 1/4 inch thick, and then put
your pieces on top of it, let it set overnight and break it up and
trim the edges. In the case of teacup parts, you may want to use a
spatula and fill the backs, first. And you may even just do that and
set them on the paper, without laying out a sheet of Devcon first.
All that depends on how much of a cavity you have. Since you’re not
going to cut the tops, like turquoise, you’ll need to be sure to keep
them clean. And you’ll want to push the pieces down so the backing
isn’t so thick, and also not so thin. Anyway, there are some various
methods, but we used to do 20 pounds of turquoise at a time like
that, it’s pretty much the standard way.