It isn't that hard to do.
Just install it first, and then look at the configuration. If you have a static IP, go to
http://www.whatsmyipaddress.com/ to get it, otherwise if you have a Dynamic IP you might need to go to
http://www.dyndns.org/ or some other place and get a subdomain and then download a client to update your IP to the subdomain every 5 minutes or so.
Once you have your IP or subdomain, you need to configure your server. Run TWGS, and then hit the "Stop Server" button. Now select the "Server" menu and choose the "Configure" option. Click on the Server tab of the Configure form, and then Choose the game port. It defaults to 23, but if you have a BBS or something using 23, use 2002 instead. Set the Admin password, unless you want other people messing up the game.
Now click on the Game tab. You can add and delete games here. Let's create Game A, shall we? Click on the "New" button. It will make "Game 1" you can change the description of it here. It should default to "A" for the first game.
Now click on the Registration tab and enter your registration codes you got.
Now hit the "OK" button to save your changes.
Now go to the "Tools" menu and select "Command Center" you will need to run BigBang to start up the Universe. Click on BigBang. Choose "Start with default data files" since it is your first game. Hit Ok. If it asks you if you registered, hit Yes and enter your codes in case you didn't enter them before. You can change the default values here if you want, etc. Hit "Z" and then Enter to start up the Bigbang. Ok, you are almost done. Now click on the Editors button and go to TEDIT. Hit "G", it should show your registration info here. You can change the turns per day here, etc. You can set other setting with "H" and "I" but I won't confuse you with those settings yet. Hit "Q" to exit and save your changes. Options "1", "2", and "3" are Gold options which you can explore later.
Now go back to the Command Center and close out.
Go back to the TWGS program and click on "Start Server" and then go to the Forums here and Announcements/BigBangs and post your IP and/or Subdomain and port number and wait for players to enter.
Go to
http://www.tw-attac.com/ to download a Telnet client and enter your IP or Subdomain and port number there and start playing in your game.
If this makes sense to you, please let me know. If not, I am not sure else what to say. Good luck.