Hello Pebeo, Welcome to Wattflyer!
A servo is hooked up in two ways;
Electronically, to the receiver.
Mechanically, to the control surface.
By controller, I'm guessing you mean to the rest of the radio system. This is the electronic system. The transmitter, which (usually) has 2 control sticks, both of which move right-and-left, also up-and-down. Generally, the RIGHT stick up-and-down movement controls the elevator, which moves the plane up-and-down. This is also called "Pitch" control.
The RIGHT stick left-and-right movement usually controls the rudder (or ailerons, but for now, let's stick to rudder control) which controls the right-and-left movement of the aircraft. This is also called "Lateral" control.
These stick movements are sent out (transmitted) to an airborne receiver, which is tuned to the same radio frequency (channel and band) as the transmitter. The receiver, in turn, converts these airborne signals into electrical impulses, sent by a three-wire lead, to each servo. The receiver "tells" the servo when to move, which way, how much movement, when to stop moving and return to netural.
So, each servo has a 3-pin female connector which must be inserted into the proper slot (port) of the receiver. Generally, the # 1 port controls the rudder, #2 the elevator, # 3 ailerons and # 4 throttle. This can vary, depending on the brand of radio.
Since this is an electrical device, it need electric power to operate. The transmitter has it's own battery, but what about the receiver and servos?
Model airplanes that have electric motors for power, also use the motor battery for the radio (airborne components, receiver and servos) power. A device called an Electronic Speed Controller (ESC), which is an electronic "throttle" also diverts some of it's battery power to the receiver and servos. This device, as you might expect, gets plugged into the receiver port marked "Throttle". So, you must hook up an ESC and motor battery to power the receiver and servos. Or, you can use a small 4 cell NiCad or NiMH battery, plugged into the port marked "Batt" for power to the radio components. Many times these small batterys (receiver batteries) come with a complete radio set, usually there is a wall charger for both the transmitter and receiver batteries.
I hope this is what you were asking about!
Here's a link to a "Radio Control Basics" site;