Hi ..
Well first of all you need to find out which ports and which IP address that application needs to communicate with. Once you have those details .. it is just a matter of allowing that access on the PIX and you also need to create a PAT translation for the internal host to make it routable on the Internet.
For example let's say that your internal host is 10.10.10.10; the public server is 203.203.203.203 and the port that the internal host needs to communicate is tcp/6200 .. then you will need:
1.- create an access-list to allow this access
access-list Inside-Out permit tcp host 10.10.10.10 host 203.203.203.203 eq 6200
2.- Apply that access-list to the inside interface of your firewall.
access-group Inside-Out in interface inside
3.- Create a PAT to allow the host to be routable on the Internet
global (inside) 1 interface
nat (inside) 1 access-list Inside-Out
The above is just an example for your reference.
I hope it helps .. please rate helpful posts !!!