by piece do you mean a geometric object (mesh)?
say like you have 2 cubes (cube1 and cube2), you put cube1 into vertex selection mode and you somehow select the vertex of cube2?
make sure you only put the mesh you want to change in the selection mode.
so hold down the right mouse button while only cube1 is selected and put that into a component (vertex, edge, face) selection mode and you wont be able to select components of cube2
if you don't want to select components that you can't see do as Genny said and switch to backface culling mode,
or you can use the paint selection tool
that's a "Ch" pronounced as a "K"
Computer skills I should have:
Maya, XSI, Photoshop, AfterEffects, Motion, Illustrator, Flash, Swift3D