This is done by overwhelming it with traffic from multiple sources. Because it comes from many sources, potentially hundreds of thousands from all across the globe, it is very difficult to block by restricting IP addresses.
There are several types of DDoS attacks that can occur, with some of the most common being:
Traffic attacks which flood a network or system with a huge number of packets. This type of attack might be combined with a malware exploit as well.
Bandwidth attacks send massive amounts of junk traffic at the target to consume all its available bandwidth and network resources, often leading to a complete denial of service.
Application attacks target the application layer of a network or system, leaving system services unavailable.