I just purchased an iPhone 5s and I have a micro sim card but it's for a sony xperia?

It doesn't seem to fit into the slot provided for iPhones so well, do I need to buy a new sim card?

The iPhone 5s uses a nano SIM. You either have to buy a new one or cut it down to size.

If you bought the phone in the USA it is most likely locked. If it is locked to a different carrier than you SIM then you can't use it.

The 5s uses nanoSIMs, not microSIMs. So yes you would have to get a nanoSIM to use.