I'm getting my own cell phone plan and an iPhone. What do I need to know?

Also, if I want to keep my number do I need to call my family's plan and ask them to transfer something? Or what?

You don't need to know anything other than how you're going to pay for everything. When you apply for the service, you can ask them to trasfer your number over. You may have to contact the old carrier and ask them to release it.