I am assuming you're a college student doing a semester? My son and a lot of his friends did a semester either in Italy or Spain, and the schools offered side trips. When they went on side trips they were usually bused. The trips he took solo or with a friend he used the train.
First: Learn a little Italian before you go! Buy Rick Steve's guidebook "Europe through the back door" for an overview and DO read it! You may also want to pick up the Italy guidebook as well. Google RoninRome.com It's the best website ever for all things Rome! There are even Facebook pages for Italy info.
There are different etiquette rules in Europe. Always greet the shopkeepers when you enter with a buonjourno, and a grazie when you leave. Do not touch the merchandise. If you would like to try something on, ask and they will give it to you, but no touching otherwise! (We Americans are touchers). If you are asking a French person a question, start with "please." This is another difference.
Do not put your purse on an empty chair in a café. Do not hang it on the back of your chair. Keep it on the floor between your feet or in your lap. Keep a very close eye on your iPhone if you're bringing one.
Here are some blogs for you to look at written by the young!:
survivinginitaly.com
girlinflorence.com
Elizabethminchilliinrome.com
Parlafood.com
These have great pointers on what to wear (no flip flops or t-shirts!) where to go, food, etc.!
You'll be making a lifetime of memories, Lucky You!!