The various approaches the core client takes are described in some detail on the Bitcoin wiki. Once you're connected to the network, your peers can tell you about more peers, so the big question is, how do you get the first peer?
There are some hardcoded IP addresses and DNS names in the client that point to mostly-stable Bitcoin nodes. If all of these were suddenly taken offline, new users would only be able to join the network by finding one peer via other means, e.g. asking a person who is on the Bitcoin network their IP via a forum, email, or in-person.
If you're wondering if a government (or other entity) could shut down the Bitcoin network by taking out a few (say, 1-10) "central Bitcoin servers", the answer is no. They could, at best, be disruptive to the network. Just to take out the DNS lookup, they'd need the cooperation of (or the ability to DDOS the servers of) the IANA (root DNS servers), or those in charge of all four of the .org (Public Internet Registry), .me (Montenegro), .be (Belgium), and .com (Verisign) TLDs. Or the government would need to be in control of your Internet connection and prevent/redirect these requests, and block the use of Tor (and other proxy/anonymization things) to bypass these restrictions.