AWStats is normally configured to run as a cron job. There are two parts to it.
1.) Run an update of the database. This ingests the log files.
2.) Generate the output. This is the part you need to look at.
Here's an example of what I do for some of the sites on my server:
00 7 * * * perl /usr/lib/cgi-bin/awstats.pl -config=blackbirds.tv -output -staticlinks >/var/www/manticore/stats/awstats.blackbirds.html
The /var/www/manticore folder is the home folder for the server's main domain (www.manticore-uk.com, this is live so go and have a look, the default site is actually empty and you'll get an error, but the awstats files are all there).
As you can see this is done with a simple output redirection. And, sorry, yes, this only really works this way under Linux. I haven't got an idea how to do this under Windows.