One of the better places to learn about how your bike works and what you need to do to keep it in good working order is the late Sheldon Brown's website. He has a section on gearing that is worth reading: How To Shift Your Bicycle's Gears

One important thing to remember while using a multi-speed bike is to anticipate the need to change gears and do it slightly before you actually need to do it. That means shifting into an easier gear before stopping the bike. Ditto just before you start up a hill. Shifting up in anticipation of needing a higher gear is less important. My trike has 30 gear selections and if you asked me to tell you what gear I was in I would not be able to give you an answer. Once you ride for a while, shifting becomes automatic and you don't have to even consciously think about it. You just do it.