Shifter(and brake) cables are made of twisted wire. As the bike breaks in,the cables get pulled tighter,and the wire twists a little tighter and lengthens(generally referred to as cable stretch,although it doesn't really stretch). This causes the shifting to be less accurate,and can even prevent you from shifting into some gears. The screws which control the limits of the derailleurs' movement can also loosen and cause shifting problems and chain drops. And chains do wear out. What you're describing sounds like the bike needs a tune-up,possibly a chain.
As Wanderer stated,
Sheldon's and
Park Tool's sites are good places to find out what to do for your bike. There are also plenty of vids on YouTube. You could also do a Google search for co-ops or 'bike kitchens' in your area to find places that can show you how/help you work on your bike.