How do I allow a specific website to penetrate my firewall?

Firstly, which firewall are you using?

Norton Internet Security

Norton is a stateful firewall, all packets are inspected and if the
request was from inside the firewall the request will be allowed back
in.  If the request was not from inside the firewall the request will
be dropped.  If you have a business need to let http traffic inside
your firewall I would suggest you change the default http port 80 to
some higher level unused port and then notife the external server of
the new port or use Zonealarm Pro and configure NAT.