.com, .net & .org domians are "pull" rather than the "push" system when it comes to Nominet and the .uk domains.
First thing - do you have a domain holding account anywhere?
If not, this is the first thing you'll want to get.
There are many companies out there that will let you setup a free account.
I use 123-reg.co.uk for all my domains at the moment - they are however not the cheapest place for .com, .net domains.
Once you've got an account setup, you make a request to have the domain pulled into your account.
With 123-reg.co.uk you literally log into your account, click "Transfer a Domain" and follow the on-screen instructions.
The various systems will send an e-mail to the registered owner of the domain name - they then just have to follow a link to agree to the transfer and a day or so later the domain should be transferred.
Most companies will allow you to transfer your domain in for free - however they will add another year onto the registration and charge you accordingly.