Never sign a blank or partially blank contract. Before paying, get a sworn statement that all bills for material and labor have been paid for by the contractor. Typically a down payment of one third of the total contract price is made with additional payments made after completion of each phase of work; final payment should not be made until work is completed and you have inspected the work.
If the work is to be financed, be sure to have complete details of the financing agreement, especially if a second mortgage of your home is used as security for the remodeling work.
