To access the squid html proxy, you just have to point your browser to port 8080 on the IP address of the ASL box, which you do via your browser's proxy config.
But if you are running ASL with just a single NIC, just to run proxies (you can operate the POP3 and SMTP proxies that way as well), the you don't really use or need the full feature set of Astaro Security Linux. Just running squid is something you can easily do on a RedHat linux box.