Rods or cables connect the ailerons to each other and to the control wheel (or stick) in the cockpit. When pressure is applied to the right on the control wheel, the left aileron goes down and the right aileron goes up, rolling the airplane to the right. This happens because the down movement of the left aileron increases the wing camber (curvature) and thus increases the angle of attack. The right aileron moves upward and decreases the camber, resulting in a decreased angle of attack. Thus, decreased lift on the right wing and increased lift on the left wing cause a roll and bank to the right.

Which gives you the idea on a aircraft which has free airflow over the wings and a free movement of roll - in a Hovercraft we do not have wings , nor a free airflow over a big surface like a wing. If we want to accomplish a similar roll and bank action on a Hovercraft  ...we would need to apply this control surface at the thrust duct exit or behind the thrust propeller - the only place where we have sufficient airflow over the control surface.   But we dod not need the high angle of a aircraft ...only a 1 or 2 degree roll / bank moition would be sufficient for a Hovercraft . The most common way is with a control surface which is in a 45 degree angle from the center out.

A roll and bank control surface would be very helpful if you go in a turn and could lean the craft into the turn before initiating the actual turn to increase the air-gap on the outer skirt section while decreasing on the inner skirt creating friction against the surface.
An other approach or solution is by skirt shifting to create same motion to the hull without the need of a control surface.

Elevators: 

The elevators control the movement of the airplane about its lateral axis. This motion is pitch. The elevators form the rear part of the horizontal tail assembly and are free to swing up and down. They are hinged to a fixed surface--the horizontal stabilizer. Together, the horizontal stabilizer and the elevators form a single airfoil. A change in position of the elevators modifies the camber of the airfoil, which increases or decreases lift. 

Like the ailerons, the elevators are connected to the control wheel (or stick) by control cables. When forward pressure is applied on the wheel, the elevators move downward. This increases the lift produced by the horizontal tail surfaces. The increased lift forces the tail upward, causing the nose to drop. Conversely, when back pressure is applied on the wheel, the elevators move upward, decreasing the lift produced by the horizontal tail surfaces, or maybe even producing a downward
force. The tail is forced downward and the nose up. 

The elevators control the angle of attack of the wings. When back pressure is applied on the control wheel, the tail lowers and the nose raises, increasing the angle of attack. Conversely, when forward pressure is applied, the tail raises and the nose lowers, decreasing the angle of attack. 

To shift a Hovercraft on its lateral axis is important to get a Hovercraft over hump ( especially on water ) to overcome its own wake and stabilize the craft during acceleration. On a hard surface the craft would be slightly tilted aft ( approximately 2 - 3 degree).
On a wet start ( starting the Hovercraft on water and accelerating from a dead stand still to overcome its own wake ) the craft will blow a "hole in the water " or in other words it will displace the water under the craft with air.
When the craft will accelerate it creates a wave in front of the skirt. Now you need to push the wave and climb over it. During this phase its helpful to be able to change the Hovercraft on its lateral axis via control surfaces.
Once you overcome your own wake ( around 12 - 15 miles speed ) you leave your wake behind you as well do not blow a hole in the water anymore.
Elevators are normally attached to the thrust duct exit or behind the propeller in a horizontal axis / sometimes slightly tilted to combine elevator and aileron in one control surface.

Rudder:

The rudder controls movement of the airplane about its vertical axis. This motion is yaw. Like the other primary control surfaces, the rudder is a movable surface hinged to a fixed surface which, in this case, is the vertical stabilizer, or fin. Its action is very much like that of the elevators, except that it swings in a different plane--from side to side instead of up and down. Control cables connect the rudder to the rudder pedals.
In a Hovercraft the rudder has to be behind the thrust exit - either duct or prop. In some applications short rudders are used to allow forward trust while creating sideways thrust to reduce craft tilt.

Reverse thrust buckets :