Bought a used iPhone 4, what do I need to do?

So I already had an iPhone 4 but it started acting up so I purchased a used one off eBay. How do I activate it, just transfer the sim over to the "new" phone and plug into iTunes? Will it automatically transfer my plan etc

No take it to the company you have your plan with they will activitie it

It should but if the person that sold it did not restore it then you might want to restore it and then transfer your data