The most common way to insulate a basement wall is with sheets of foam insulation sometimes called styrofoam, rigid foam or XPS. Sheets of foam insulation come in several different thickness choices and they can be found in the insulation section at most home improvement stores. They may be sold in 4'x8' sheets or sometimes may be cut down smaller for easier installation.
These foam sheets may be attached directly to the concrete. They are most commonly glued directly to the basement wall with a caulking gun and glue that is designed specifically for rigid foam. Rigid foam insulation sheets will cut easily with a razor knife. Some even have printed lines on the foam sheet to help with installation.
When installing basement insulation of any kind it is important to make sure all basement walls are dry and there are no water leaks. Installing rigid foam as basement insulation is a fairly simple process. Insulation sheets should be installed vertically. Most basements will be approx. 8 feet tall. You may have to trim sheets a little to fit around floor joists or other mechanicals in your basement. Glue each sheet to the basement wall only after you have determined it will fit properly. Apply the glue directly to concrete basement walls and install each sheet. You may also want to use insulation tape to cover the seams. This can also be found in home improvement stores.
No vapor barrier is required for basement insulation. In fact installing plastic will just trap moisture behind your walls. After you have installed rigid foam you are ready for framing.
Spray Foam Insulation
Spray foam insulation can also be an option for insulating a basement. Spray foam is applied directly to concrete and expands to fill any cracks or crevices. Spray foam is usually a very messy operation. If you decide to insulate with spray foam you should skip ahead and get all your framing done first. Be sure to leave several inches between your framing and the concrete basement wall. This will allow foam to expand and fill the cavity between studs and basement wall. Spray foam for a basement is not really a Do it yourself project because of the equipment involved. You should probably hire a professional if you decide to insulate with spray foam.
Fiberglass Batts Insulation
This type of insulation is never recommended for basements Fiberglass batts are air-permeable. When fiberglass batts are installed in contact with concrete, the moisture in the interior air condenses against the cold concrete surface, leading to mold and mildew. Fiberglass batts and mineral wool insulation should never be used in a basement. There is however one exception to this rule. If you have a garden style basement or walkout basement the fiberglass can be installed above grade on the wall above the concrete walls.
If your basement walls get wet you have a moisture problem. You will need to solve the moisture problem before you insulate your basement. Basement walls should never be insulated until the water-entry problem is solved.