How can I find out what domains/websites a person owns?

I’m sure it’s possible, but I would imagine you’re going to need someone whose specialty it is to uncover this sort of information.

When you register a domain, you can make your name and contact information private. So short of a google search to see what websites come up with claims of ownership, you probably can’t unless you have inside access at ICANN.

If you are willing to pay, domaintools will do this for you.
If you want it for free, install “DiG”, read the manpage, and go to town. But first read up on how DNS works. If you have a UNIX or Linux machine dig is probably already installed. It’s possible but not easy to install it to Windows. In Windows the “nslookup” command may offer similar functionality but I have not found it with a brief search.