If you're running apache, adding this to your configuration will clear up the broken links-
The other advice was good. It's a Catalyst application and there are many tutorials and guides, some in the Catalyst docs, for how to deploy them. Proxying is probably the best all around solution but fastcgi is probably the easiest. Here's a sample apache config for running one out of a user's home dir with local::lib.
# Start gitalist with-
# perl -Mlocal::lib=/home/moo/perl5 ~moo/Gitalist/script/gitalist_fa
+stcgi.pl -l /tmp/gitalist.socket -d
FastCgiExternalServer /tmp/gitalist.fcgi -socket /tmp/gitalist.socke
Alias /git/ /tmp/gitalist.fcgi/