Nail pops in the walls
Over time, the nails that hold your drywall to the framing may start to protrude from the walls. The best fix is to remove the nails and replace them with drywall screws. Then, fill the screw holes with spackle or drywall compound ("mud"). Then prime and paint each spot.
Cracking/Peeling Drywall Seams
If a drywall seam was not well taped when installed or seams have just begun to crack over time, you can repair those areas. Use a utility knife to remove the tape from the damaged seam(s). Install new tape (mesh is best for patching). Apply drywall joint compound, 2-3 coats. Sand, prime, and paint to match. If the paint is older, you may need to repaint the whole wall or ceiling for consistent color.
Paint Drips on walls
If you have dried paint drips on your walls, you can simply sand them down and repaint. You may need to apply a bit of spackling paste to smooth out the spot first, then prime and paint to match. If you need get paint colors matched, get a chip from the wall about the size of a quarter and take it to a home center or paint store where they can match the color in the computer.
Water Stains on Ceiling
Stains on your ceiling indicate a water leak from plumbing or a roof above. If you have addressed the cause of the leak, you are ready to repair the drywall and paint. If the leak was minor and you just have a stain, but no soft/damaged drywall, you can simply repaint. It will likely take several coats of a product like Kilz to fully cover the stain. If there is any soft or crumbling drywall, remove that section of drywall to the nearest joists. Inspect the area above and around the damage to be sure there is no mold. Install a new piece of drywall and apply seam tape and joint compound. Sand, prime and paint.
Mold Growth Showing on Walls or Ceilings
If you see growth of what looks like mold on any of your walls or ceilings, you should get it tested before doing anything else. Mold can cause serious allergic reactions and health issues. You can have a professional come in to examine and test the area or you can buy a test kit at any home center and test it yourself. One of the most important things initially is to determine the nature of the problem and to not disturb any moldy areas. Once mold spores are stirred up and become airborne, that's when they pose the greatest health risk. Mold is indicative of a water issue somewhere behind your walls, so you will need to be ready to find the cause of the problem as well. Don't attempt to remove or treat any mold until it has been tested. If it is indeed a harmful substance, be sure to have it properly removed by remediation professionals. After removal, make sure you find and fix the source of the water that caused the mold issue.