There are 2 different functions that are often confused.
Registration transfer -- this transfers the domain registration from one registrar to another. This is who you pay each time the domain registration expires (and who should be reminding you the domain is soon to expire). (note: transferring the registration shouldn't necessarily change the nameservers.)
Nameservers change -- In its simplest form, this determines where the domain is being hosted. If you change the nameservers, hosting moves but that doesn't change where the domain is registered.
Anytime there is a change of namesservers there must be "propagation". However how long propagation takes could be anywhere from "seconds" to 72 hours... average is probably a couple hours. There are several factors that affect this, TTL (time to live) being the greatest. At dreamhost we have no access to our domains TTL settings.
You can check both who the registrar of a domain is, and the nameserver settings by using a WHOIS service. Oddly enough the one I use most often is network solutions: http://www.networksolutions.com/whois/index.jsp The header of the domain record will indicate who the registrar is, further down usually near the bottom you will find the domains nameserver settings.