Since you have both client and server programs, you can simply run them both on same PC and test them just like they would be on different machines. (use "localhost" or "127.0.0.1" as IP address of server)
It's enough to test program algorithm, and once it work on same PC, it should actually work on any two machines over internet/LAN.
Of course you should understand how networking actually works. Whoever you are connecting, must be visible to you. If you are going to connect via internet, server's IP address might not be enough. Something like http://www.showmyipaddress.com/ might show ISP's front, "white" address. And user, who run the server might have "grey" IP address, behind a NAT. So if you are going to use something like showmyipaddress.com , check your real IP address by typing "ipconfig -all" in windows command line. If ipconfig shows same IP, there are high chances it will work over internet (just check your firewall).