There isn't really an answer to this.
A Distributed system is more of an ideology (ehh... not sure of a better word?), rather than a fixed implementation.
For example, a Distributed system (in my mind) is the term used to identify a system of any size that can be split in to smaller units for improved reliability, performance or uptime.
In addition, where it is appropriate, a distributed system will also have load balancing\high availability and similar technologies built in.
As for how they work, it would be completely different depending on what the system is providing.. e.g. a MMORPG distributed system will be completely different to a banking distributed system, but, they are designed to do similar things in the end - maximum uptime and resilience.
As for giving you more specific answers, I really need to know what sort of distributed system you are interested in... You are sort of asking a question that is far too broad to give a single specific answer.