Use logging module (http://docs.python.org/library/logging.html):
import logging
logger = logging.getLogger('scope.name')
file_log_handler = logging.FileHandler('logfile.log')
logger.addHandler(file_log_handler)
stderr_log_handler = logging.StreamHandler()
logger.addHandler(stderr_log_handler)
# nice output format
formatter = logging.Formatter('%(asctime)s - %(name)s - %(levelname)s - %(message)s')
file_log_handler.setFormatter(formatter)
stderr_log_handler.setFormatter(formatter)
logger.info('Info message')
logger.error('Error message')