Despite it's name, as far as I know Apache::Session does not have any dependancy on Apache. It simply uses Storable to tie a stored hash to a session id. You then need to stash that session id in a cookie/url variable or whatever takes your fancy.

Take a look at the HTTP_COOKIES section for CGI.pm for it's handling of cookies, assuming your web browser accepts headers set by cgi's in the usual (CERN/NCSA) fashion.