A. There are different types of insulation, but I assume you are talking about fiberglass batts that come with a facing on one side. The facing may be just paper or paper with a liner that provides some vapor barrier functionality. Some batts come with a plastic wrapping all the way around, and some come with no facing.

The main thing to keep in mind is that a vapor barrier should always be installed on the interior side of an exterior wall. If you are using insulation that has a vapor barrier facing, then that will face into the room. Paper faced batts provide flaps that allow you to staple them to the studs so that they will not be dislodged during later phases of the work. Batts that are not faced or only faced with paper should have a 4 or 6 mil sheet of plastic (visquene) stapled on the room side of the wall. The air inside a house usually contains more moisture than the air inside the wall, and you want to keep that moisture out of the insulation. If the vapor barrier is placed outside of the insulation, the colder air behind the insulation will cause condensation on the barrier, leading to damp walls. This will promote the growth of mold and mildew inside the home and can lead to health problems.

You may want to check out this answer about framing basement walls.