How do hydraulic machines work?

There's so much information out there on the web that it's unlikely any question you have would be unanswered somewhere so when someone asked about hydraulics and how they worked, I thought I'd do a quick search and get the answers for them.

"How Stuff Works" comes immediatley to the rescue:

From backyard log splitters to the huge machines you see on construction sites, hydraulic equipment is amazing in its strength and agility! On any construction site you see hydraulically operated machinery in the form of bulldozers,backhoes, shovels, loaders, fork lifts and cranes. Credits: HowStuffWorks "How Hydraulic Machines Work"
 

Follow the link to see a fantastic presentation.