Outside the USA everything is GSM, and you don't need your provider's approval to use your phone: you just put your SIM card in it.
The only thing you need to be aware of outside the USA is that:
- American CDMA phones don't work, because nowhere else has CDMA
- Most GSM phones can be locked to only accept the SIM from one operator; phones you buy outright are unlocked, phones you get with your contract are locked, and with preowned phones this is something you should ask about
- 4G will only work if your phone has the correct antennae, which vary from country to country. A USA-edition phone may or may not be able to get 4G in Singapore, Norway or Australia, even if they sell the same model there.