How Can I Transfer A Domain Name That My Friend Bought Into My Name?

Me and a friend of mine used to co-own a website. I paid for all the hosting and such like which was registered in my name and he purchased the domain name, which was registered in his name. Now he wishes to leave the website and has agreed to transfer the domain name to me. Only thing is we don’t know how to formally go about changing the ownership details of the domain name.
Can anyone help?