Change nameserver

I registered domain here at dreamhost, but I would like to host it elsewhere. This is what I need to do, according to my new host:
“You can simply change the nameservers on your domain or request that your current registrar change them for you.”

Is this something I can do? Or do I have to contact the dreamhost staff?

You don’t need to contact the staff for that. Just go to the Domain Registrations page and then click the “Modify” button next your domain to modify its nameservers.