Not all US phones will work in Europe. Some US phones work on a totally different and incompatable system. You need to contact your provider and ask:
1) Will my phone work in Europe?
2) If Yes, how much will calls etc. cost.
If yes, and the charges are OK, you are good.
A SIM card (click here for photo) is a little chip which goes in your phone (usually under the battery) and sets up what the phone ID is. It defines your provider, phone number etc. If you move the SIM card to a new phone, that phone has your phone number and is charged to your bill.
All phones in Europe have a SIM card. Not all phones in the USA do. If your phone hasn't got a SIM card it definately cannot be used in Europe.
If your phone and provider will not work in Europe, or are too expensive, you have 2 options:
3) Buy a new SIM card for your phone after you land and put it in your phone. This will give your phone a "brain transplant", it will now have a new phone number (from whatever country you buy the card in), and you will pay bills to an new provider. You will need to check your phone is compatable and "unlocked" for this option.
If your phone will not take a new SIM card, you will have to:
4) Buy a new cheap phone after you land, with a SIM card in it. This will cost ~€20. As above, you will have a new phone number and provider.