Hi Nancy, welcome to TE.
a good place to read about bike stuff is http://www.sheldonbrown.com/ Sheldon Brown's website. He talks a lot about gearing.
If you have a cadence meter on your bike computer (you HAVE a bike computer, right?) you can start becoming aware of how hard you are pedaling.
If you find yourself muscling yourself up a hill, you go to a lower gear. Try out all your gears on the flat first, then later on a hill.
as for mirrors, I would be lost without the 1" square mirror I have duct-taped to my helmet. Sometimes when I go for a walk, I try to look into it (it's not there) that's how dependent upon it I have gotten. It's great for being able to ride in traffic..