The states appoint delegates who meet, elect their own convention officers, set rules of procedure, and formulate amendment proposals.
Upon adjournment, the proposed amendments are transmitted to Congress which then passes the proposed amendments to the states for ratification. Congress decides whether the states will ratify by state legislatures or state ratifying conventions. Go back to my boilerplate post for details.
So, basically, an Article V Convention, or Convention of States, substantially limits the federal involvement which is a good thing!