If you're the owner and the one who reported the iPhone as lost in Find My iPhone, entering your Apple ID and password will enable you to restore the iPhone and set it up with the last backup you made.
If the iPhone is one that was reported lost by someone else, the Apple ID and password of that original owner will be necessary to restore the iPhone to use. Without the Apple ID and password of the original owner, there is no way to activate and use the iPhone. This is called iCloud Activation Lock and is a security measure implemented by Apple when iOS 7 was introduced. It's designed to prevent anyone but the original owner from erasing and using the iPhone.
There is no way to bypass the Activation Lock without the Apple ID and password of the original owner. None of the iCloud Activation Lock bypass methods you see advertised on the Internet will work.