Damaged Vinyl Siding
If you need to replace a small section of your vinyl siding, it's not very difficult. There is a siding removal tool available at home centers for about $10 that will help you unhook the damaged siding section. You can remove a small section and replace it with a short piece that overlaps the existing siding. You can cut out a section using snips or an oscillating saw. Just be sure to cut in a spot that will keep the joints staggered. Then use the siding tool to help you lock in the new piece to the existing.
Water Stains on Ceiling
Stains on your ceiling indicate a water leak from plumbing or a roof above. If you don't have any plumbing above the stained area, the problem is most likely a leak in your roof. Remove the stained section of drywall to the nearest joists. Inspect the area above to find where the water is entering. If it's a flat area of roof above, you may have damaged shingles, felt underlayment, or roof decking. If it is in an area where two different pitches of the roof meet, you may have some damaged or missing flashing. In either case, you should call a licensed roofer to inspect and repair. Once you are sure the leak is fixed, install a new piece of drywall and apply seam tape and joint compound. Sand, prime and paint.
If water is flowing over the edges of your gutters and not flowing into your downspouts, there are several possible problems. The most common is that your gutters are clogged with debris and need to be cleaned. Check your gutters and clean any leaves, twigs, etc. If this is a recurring problem, you may want to consider some type of gutter guard to block debris from entering the gutter. You could potentially have an issue with the downspout or the outlet from your gutter into the downspout. There are products available to address that as well. Lastly, the slope of the gutter may not be sufficient. Your gutter should gently slope towards your downspouts in order for water to properly drain (water won't run uphill or level). If they appear to be level or sloping the wrong way, they will need to be removed and re-installed with the proper slope.
Spots on Roof With No Snow
If it's winter and you've had a significant snow, take a look at your roof. If you notice a few areas where the snow has melted or never accumulated compared to the rest of your roof, you may have some missing insulation. If your attic has some areas with insulation missing under the roof, the heat will be able to escape through the roof, creating a warm spot and melting any snow that falls in that area. If you notice that on your roof, it's a good indicator that you should check the insulation in your attic. You may be losing quite a bit of energy in those spots! The simple solution is to add insulation in any deficient areas.