Basically DoS is Denial of Service, and DDoS is Distributed Denial of Service.
Also, there are tons of DoS/DDoS's, from SYN Floods, where the third part of a three way hand shake is never answered, causing the request to stack, from hundreds of thousands of users, along side with all us legit users getting piled up in those ques...
Pings of Death, which are easily blockable by denying pings all together....
Smurf attacks are nice. Basically it uses broadcasts, and when they send a response back to the originator, the originator spoofs itself to be the victim, causing the victim to loopback to itself (which you can;t block or you destroy that interface, you have to block the originator/attacker and clear the loops) and basically causes the interface to send more and more broadcasts to it self which it answers and starts all over. So in a mere matter of minutes one interface can be caught in 1 million + loops.
Land Attacks are the original Smurf Attacks, because in the packet headers was the same destination and originator info, but 99.9% of firewalls catch this.
Less common but still effective is Teardrop Attacks. Basically you send fragmented packets and it then does various things when the packets are assembled, from just to many fragmented packets, to assembling to form a malformed data pattern (think of 1/0 in binary.) Old systems would have a kernel panic due to some of the coding, bringing down the systems interface then entire OS.
There's more attacks than that, but that's the most widely used. Smurf is the hardest to fight because with zombie networks, you attack in waves. Have the first 10 machines start, and as they start to block you roll out 10 more machines. So you are forcing them to do two things: 1 block addresses and 2 clear loopback broadcast requests. So then they finally block the original machines, 40 more are online.
The thing is, if you want to really do it right, you do not attack sole interfaces/devices, you attack servers, firewalls, gateways routers, isp controlled points, to the point where it's hundreds of public addressed servers are being attacked a long side dozens to hundreds of network components inbetween them and the WWW.
So think, next time they aren't just DoS'ing your router/computer, they are DoS'ing your actual Cable/DSL Modem and your ISP's gateways, and possibly even their DNS all at the same time.
If they collapse one point, they did their job and took you offline. You come back they start all over.
This is a lot easier said to with so many kids able to access computer labs and have friends over the internet do the same thing.
Not to mention Zombie Machines and people in Foreign countries with easy access to multiple machines and no real Internet Piracy Laws.