Before you get too far into hosting your own, there's a decent handful of mohawk servers out there you can join (not as many as southwest but they do exist).
Now if you do want to go forward and host your own run8 server, you will need Three IP Addresses:
#1 - Public IP Address (you will share this IP with your friends) - To find this, google "What is my IP address" and google's pretty good about telling you what that is.
#2 - Private IP address of the PC running Run8 - this is the address used locally in your home network - To find this, open a command prompt and type "IPCONFIG" (this will be the IPv4 address, and quite frequently will look like 192.168.0.2)
#3 - The Private IP address of your router (This is found with IPCONFIG as well, it is the "Default Gateway" and is frequently 192.168.0.1)
Now for the hard part:
You need to log into your home router, and forward traffic for port 15197 from the internet, to port 15197 on the private IP address you found n step #2 above.
This isn't terribly hard, but many people do not know how to get into the home router to configure it, so this can add an extra layer of complexity.
Routers vary, but most will have a website of one kind or another.
You may need to google that for your brand of router. (Some routers may have this info on a sticker on the underside of the router)
If the router hosts it's website on port 80, you can just open a browser and enter http://<IP address from step3> (Do not type the <>)
If the router uses a custom port for its website, you'll need to add that.
For example, if the router uses port 8080,
you'd enter http://<IP Address from step3>:8080 (Don't type the<>, but DO type the : )
example
http://192.168.0.1:8080
From here the steps vary too much from router to router, but I suspect if you google or search youtube for your brand of router + the words "Port forwarding" you'll find a step by step tutorial that should walk you through everything for your specific router.