However, the contractor charges and material rates fluctuate from one state to another. On an average, the cost per square foot to finish basement range somewhere from USD 29 - 32 for basic remodeling to as high as USD 50 for installing upgrade features.Do-it-Yourself Basement Finishing.n an average, the cost per square foot to finish basement range somewhere from USD 29 - 32 for basic remodeling to as high as USD 50 for installing upgrade features. Do-it-Yourself Basement Finishing.