If you want to be contacted via your USA phone number, you should add an international calling plan to your line. Data too if you want. Familiarize yourself with the cost of those plans.
If you want to get a local number there, you can get your iPhone 4S unlocked to use another SIM card. You would call customer service and ask for the global services. If you meet the requirements, you can request Verizon Wireless to SIM unlock the phone.
There are other discussions about this more details in this space of the community forum.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.