I have called VZ to unlock my 9530 because I need to travel oversea. When I get there, do I just get a new sim card from the local carrier and replace the original sim?
Yes. The SIM card you have in there now is not even required for your phone to work in the US. It's there so Verizon can sell your their international coverage, if you choose to use it.
You can use a service, such as offered by UniquePhones, to unlock your phone.