This is a website that can give you tips on how to forward your ports on just about any router. First you pick the manufacturer(they are in alphabetical order). Then, you pick the model number. This should be somewhere on the router itself somewhere. Then it'll show you how to do it.
http://portforward.com/english/routers/port_forwarding/

Just in case you can't find the right guide, here is the address you need to go to, to get to your routers settings. First a window will pop up asking you for your password. Usually the username is admin, and if you didn't write your password down then shame on you(Iirc the default password is usually password).
192.168.1.1/
My current router is 192.168.1.2/, so you may want to try this too if the first one doesn't work.
If you really don't know your password, then you may need to call your router's company or your ISP and they might know it.

So, when you get there you need to know just a few details to forward your ports. First you need to put in "Terraria" in the application name. Then, you need to put in the port you want to open(7777). Last, you need to know your network IP. Finding your network IP can be different for different computers, but to point you in the right direction, you can first click the little bars icon in the toolbar of your computer, then click "network and sharing center". Then you click on connections, and then details. This would be for a windows 7 computer, but I'm not sure what it would be for other ones(this is why it would be helpful to go to the site up above).

Here is just an example of a linksys E3000 routers settings where you put in the information to forward your ports:
Next you need to find the correct IP address to give to the people you want to join your game. If you have Hamachi then don't use the IP that that gives you, just go to whatsmyip.com or type in "what's my ip" in google and you will find the correct ip address.

I'm not sure if you have to have a server program to do this, but it would certainly help. If you want, go to terraria.org, and they should have server software to help you connect with other players.