What did you try yourself??
cat logfile | grep '^11' > november.txt
$ cat logfile | grep '^11'
11/12/2003 /web/scripts/mms_script
11/13/2003 /web/scripts/mm_scripts
Or, if you want the month found automatically:
$ cat logfile | grep "^`date '+%m'`" > "`date '+%B'`".log
The above samples can be run from the command line. Up to you to script them
