Install a large, well-lit chandelier in the ceiling's center. Select one that is large enough for two-story spaces. Many of these styles of chandeliers are common in large entrances or great rooms of homes. The chandelier you select shouldn't be one of the smaller models typically placed above kitchen tables. It should have bright halogen lights and enough cable and cord to hang in roughly the middle of the second story.
Place wall sconces on each side of an entrance into the room to give it a warm feel and also provide upward, indirect lighting. Wall sconces are available in virtually every style and are ideal because they don't take up floor space. When mounted against the wall, a sconce will send a beam of light up the wall; when the wall is painted in a light color, the room will appear brighter.
Stand one or more floor lights in the room in convenient locations, such as next to a couch or chair. Avoid overusing floor lights, as they will sacrifice floor space and can be difficult to clean around. They are, however, a useful way to add light to the room if the room serves a practical, rather than only decorative, function.
Hang a large mirror on an open wall to help redirect the light from the fixtures in the room. If possible, place the mirror across from a wall scone so that it can pick up and redirect the light easily. Mirrors also give the illusion of the room being larger than it is, which is ideal in any size of room.