During the initial era of air travel how do the pilots/Navigation officers would communicate with ground stations?
Do they use radio communication? Or Telegraph was used?
Radio was not widely used until the 1930s, before that, mostly light signals were used. Early ground support aircraft in WW I could drop little notes which were pencilled by the observer, stuffed in a small capsule to which a streamer was fitted, and that was dropped as closely as possible to the troops which should get that message. This method was still used in WW II, when most aircraft had radio, because only specially equipped ground troops had compatible receivers.
The first regular flights by night were 1921 for the air mail connection between Omaha and Chicago, and electric flood lights were positioned along the flight path. When Lufthansa opened the first night connection between the Reich and East Prussia in 1926, they posted burning oil drums along the way to mark where the pilot had to fly. Communication the other way (air to ground) was not possible on those flights.
The first air-to-ground radio communication used morse signals, and this is the origin for these strange three-letter names for things like local air pressure at the ground (QFE) or pressure corrected to sea level conditions (QNH). There was a whole lot more of those, including some to order coffee before landing, but they are no longer necessary. Read all about it here.
While radio was available (meaning it existed) it did not exist in a form usable by early aircraft.
If you are talking early-early travel, not commercial travel, communication was not necessary. Navigate to the destination, circle the (farmer's) field to check for livestock, then land. Communication with other aircraft was not necessary as there usually were no other aircraft.
As things progressed, morse code became practical. This was when cockpit crews required both hands to count.
Up until World War One, there was no radio communication between air and ground, or between planes. Communication from ground to air was done by means of light signals.
From 1915 onwards aircraft were used as artillery spotters which involved Morse code wireless signals one-way, (from the aircraft to the ground). There was no communication from ground to air, and the air-to-ground communication was limited to simple codes. The only form of air-to-air communications was signals such as 'wing-waggling'.
Air-to-ground and air-to-air spoken radio communication became common between the wars, and was widespread in major air forces at the start of it.
Military aircraft frequently used radiotelegraphy (Morse code) well into WWII, if not 'til the end. The binary nature of it (on/off constant amplitude signal*) gave greater effective range and more resistance to degradation by static than radiotelephony (voice). Most aircraft had voice radios for communication with nearby friendly aircraft and bases, but relied on Morse code at long ranges.
* shades of digital transmissions today!
In World War 1 there were aircraft spark gap transmitters and the pilot could send messages in Morse code to receivers on the ground but he could not receive wireless (now called radio) signals. There was limited communication from ground to aircraft using the following three methods; Ground Strips. Lamp Signals. Poppet Panels. The pilot had to fly and watch for signals at the same time. Ground strips were white sheets 3 metres by 300 mm (10 feet by 1 foot) or larger. They were laid out as patterns or letters with a letter for such messages as 'Your (wireless) signal is weak' or, 'Repeat last (wireless) message' or 'I am not receiving your signal'. Lamp signals, used later in WW1, used 'Lucas' signalling lamps. The operator aimed the light beam at the pilot when he thought it would be visible to him and send the message in Morse Code. The Poppet Panel was a canvas shutter arrangement fixed to the ground and was worked by pulling a cord which made a white patch visible from the air. When the cord was released the panel showed a black patch. By pulling and releasing the cord the operator could send Morse Code messages to the pilot who had to fly with one hand, look over the side and write down the letters with his other hand. It was a difficult task.