Hydraulic pumps basic design is a piston in a cylinder that exerts pressure on an incompressible liquid (usually oil), and the force is transmitted to another piston which will do something useful for you. The force is usually multiplied in the process, therefore the second piston can achieve much more than the first. To add force multiplication, the relative size of the pistons is increased.

The pipe containing the oil can be all sorts of lengths and shapes in a hydraulic pump which is very useful because they can be used in almost any system design. The pipes can also be branched so that the master piston drives two or more slaves.

The oil needs to be free from air bubbles because if a piston is used when bubbles are present, much of the force is wasted compressing those bubbles rather than driving the second piston which is hardly an efficient way to go about things. Most pump failures are because of oil contamination of one sort or another. The oil reservoirs should be made from stainless steel or aluminium to prevent corrosion and reduce the chance of oil contamination.

You may not know it but you probably own a hydraulic pump. Cars use them for the braking system. When you push down on the brake pedal it pushes two master cylinder pistons which each drive two slave pistons (there's one at each wheel).