Every vessel is different, indeed, but the physics never change and so you can assume certain behaviors will be found (all else being equal of course).
On a single screw vessel, assuming a right hand wheel, the vessel will have a tendency to swing its stern to port at first, as the pivot point is amidships when the vessel is dead in the water and the transverse thrust of the propeller causes the stern to move laterally when turns are first applied. Once the vessel gains astern momentum, the pivot point moves toward the stern, and as anchorman says the most effective way to steer will be by applying thrust at the bow using a bow thruster or a tug. As the vessels’s astern speed increases, the rudder becomes effective enough that you can counter the transverse thrust produced by the propeller and also steer the stern to starboard if you wish. This behavior of course varies from vessel to vessel, depending upon numerous factors, but a single screw ship can be successfully backed to starboard. You can also “back and fill” by using the rudder and ahead engine commands to “kick” the stern one way or another without taking too much way off.
A controllable pitch (CP) propeller on a single screw ship is a whole different animal, though. A CP ship will tend to back to starboard as the propeller rotates in the same direction at all times. Most, but not all, CP ships have right hand turning wheels. CP wheels are also notorious for having much less backing power than fixed pitch wheels, so you must be careful.
A vessel’s trim also affects the way she steers. A single screw ship in ballast will be more challenging to control moving astern as the wetted surface area of the rudder is much less, she has much more windage, and is much lighter than when in a loaded condition. Single screw vessels also back into the wind, so you must be careful to consider that when trying to steer while backing. In those cases it is best to plan your astern movements with the wind in mind, if you wish to be successful.
A twin screw vessel is best steered astern by using different power settings on each engine, or setting the engines up in a twist and using more astern power in conjunction with bow thruster inputs… The rudders on a twin screw vessel will also be of use at higher speeds due to the same sheering effect that a rudder on a single screw ship has, although the smaller surface area of twin screw rudders can make this effect less noticeable. Some newer large twin screw ships (tankers, in particular) have independently controllable rudders that can be set at different angles, allowing some very creative use of engines and rudders when moving astern.