Try this link out.
| Nintendo - Customer Service | Wii
It walks you thru just about everything.
You would enter everything (I think) exactly as you get it back, except you need to change the IP address to something different. So if your laptop was 192.168.0.44, you would set up your Wii's IP as 192.168.0.45. Now your college may have a someting other than the first three sets of numbers for you static IP. Just make sure they are the same.
You would keep the Subnet Mask, the Default Gateway, and both DNS servers the same as what you get on ipconfig/all.
Again, you just need to speak with the IT department to find out what type of security they use, and just ask them for a seperate username and password for your Wii.