How does an international SIM card work?

I'm going to study abroad this semester in England and I need help deciding what I will do about my phone. I have an iPhone 5 and I want to use that when I go abroad. I was thinking about changing out the SIM card instead of paying international fees, so how do SIM cards work? What will I have to do before I leave and once I get there? And I'm confused about whether or not my phone is locked.
Also, if I get a new SIM card, what will be saved on my phone and what won't appear unless I put in the old SIM card?

The SIM card identifies the subscriber. It tells the phone and any cell networks who you are and which telephone company is your home carrier. The card can contain restrictions on which networks you're allowed to use (typically your own carrier's network, plus any other networks worldwide with which your carrier has roaming agreements).

When in England, you can save money by subscribing to a plan that provides a SIM for a local carrier. However, this will change your telephone number.

Modern smartphones store everything in the phone, so changing the SIM card doesn't affect anything except your telephone number and the cell networks you can use for calls (and the carrier that bills you). Contacts and such stay with the phone.