There are many signs that your roof could be in disrepair and in need of replacement. Some of the more obvious signs are missing, damaged or decaying shingles, leakage after hard rains, and stains on interior walls and ceilings. A roof in need of replacement will often show up in your energy bill, due to inefficient heating or cooling of your home.
Have the situation looked into as soon as possible. What may not look like much damage to you, may actually be. There could be other things going on under the surface that could take some time to fix, so the sooner the better and the less expensive.
Depending on the type and size of the roof you have are having installed. It could take a couple of days, up to a couple of weeks, weather permitting.