Drywall holes of a sufficiently small size can be patched by small drywall patch kits. These kits are sold in most home improvement stores and are typically used on holes that are not more than 2 to 3 inches in diameter. They are self-adhesive and can be applied over a small hole, then skim-coated with joint compound. Sand the compound once it dries and paint the area.
There comes a point in drywall repair where it becomes easier to replace the section of drywall, rather than attempt to patch a hole. If you are looking at a hole from a large 4- or 5-inch sewer pipe, consider replacing a larger section of drywall. Cut the drywall back to the nearest studs in a rectangle around the area. Screw in a replacement piece of drywall of the same diameter and patch the seams, using joint compound and drywall tape, before repainting the area.
A sewer pipe that has been removed from a basement or cellar wall can leave an unsightly hole in the concrete. If the hole is small, it can be patched, using patch material such as polyurethane foam. Your local home improvement store should carry numerous commercial products for patching small holes and cracks in concrete. These materials are typically easier to work with than concrete and, in small applications, can be just as structurally sound and waterproof.
Larger holes, such as those left from sewer pipes of 4 inches in diameter or more, necessitate mixing concrete and filling in the hole by hand. Remove any debris or loose concrete from the hole, using a wire brush. Fill the holes using hydraulic cement, which expands as it hardens. Smooth the hole to the wall before it cures as, unlike joint compound, it cannot be easily sanded smooth.