Well, no I'm not sure who nominet really is and why they would be asking you for anything.
Let me explain a couple of the terms quick.
An IP address is kind of like your telephone number...only for the computer. Say I wanted to call you, I'd have to dial a number and that number would ring at your phone. now say I want to see your web page, I use your IP address and thats how my computer knows exactly where to go to find your webpage.
Of course...nobody would be very happy if they had to remember all these numbers just to search the web all the time...this is where DNS enters. When I open my browser and tell it I want to see
http://www.yahoo.com, the first thing my computer does is send that request to one of the DNS servers in my list to resolve the address. The DNS server has a list of records containing host names to IP addresses. Once the DNS server finds
http://www.yahoo.com, it then tell's my computer, "hey...if you want to see what's at
http://www.yahoo.com, ask this computer: 69.147.114.210". Now my computer "dial's" that IP address and will display the webpage for me.
Keeping this in mind, just change
http://www.yahoo.com to whatever your registered DNS entry is and the IP address to whatever your external IP address is. So all you should really need to do is tell whomever you registered your DNS to change that host name to point to your home IP address rather than the host you used to have.
Hopefully this is making sense
once you have that done, now you just need to make sure everything is working on your computer to basically "answer" the call when a computer is trying to view your page.
I currently host my own web page from my PC/server and to be honest...It's a pain to maintain. Granted this is not a dedicated machine and i'm often playing games or doing some video editing....but every time I install something new I won't think about IIS and here it shut down the site for weeks and I never knew it. (needless to say I don't have very many interesting things on my site huh!

)
OH! another thing you'd have to worry about is your connection to the internet. Are you using Cable, DSL, or do you have a T1 hookup?