Open a command prompt, type ipconfig. It's one of those...
Depending on what network adapter you're using (dial-up, ethernet etc.)...that'd be your IP. If you have a router, it may have a firewall that is blocking it (that's a whole different story!)...
I'm not sure about no-ip, but
http://www.dyndns.org/ gives free domain masking etc. Probably the same thing. Your IP can be either dynamic or static, and if it is dynamic, you can download a program to automatically update it when it changes (they have a list of them there for you--all free/well, most). And what they are giving you is a sub-domain (I'm guessing), but it should work. You'd need to login to wherever (if you're not using the auto-program), and give it your current IP.
I hope that makes sense, I'm not a good teacher!