Выводим время, уровень ошибки, файл и строку вызова, ну и естественно, текст сообщения:

import logging
logging.basicConfig(format = u'%(filename)s[LINE:%(lineno)d]# %(levelname)-8s [%(asctime)s] %(message)s', level = logging.DEBUG,  filename = u'applog.log')

logging.debug('This is just a debug')

via http://habrahabr.ru/post/144566/

upd: лучший пример со stackoverfow :

import logging
log = logging.getLogger("mylog")
log.setLevel(logging.DEBUG)

formatter = logging.Formatter(
    "%(asctime)s %(threadName)-11s %(levelname)-10s %(message)s")
# Alternative formatting available on python 3.2+:
# formatter = logging.Formatter(
#     "{asctime} {threadName:>11} {levelname} {message}", style='{')

# Log to file
filehandler = logging.FileHandler("debug.txt", "w")
filehandler.setLevel(logging.DEBUG)
filehandler.setFormatter(formatter)
log.addHandler(filehandler)

# Log to stdout too
streamhandler = logging.StreamHandler()
streamhandler.setLevel(logging.INFO)
streamhandler.setFormatter(formatter)
log.addHandler(streamhandler)

# Test it
log.debug("Some message")
log.error("An error!")
try:
    something()
except:
    log.exception("An exception occured!")

via http://stackoverflow.com/questions/4722745/logging-between-classes-in-python