International Communication
With the Space Age barely ten years old, space-based communication is limited. While geosynchronous communication satellites are around, they are limited in the number of overall calls that they can take - sometimes as low as single figures at any one time.
As a result, most international communication is done by line of sight microwave relays and telephone calls. While International Direct Dialling is increasing, many calls to less connected countries involve contacting the operator, asking to be connected to an overseas exchange, then waiting for them to call you when it is ready. These calls can be pretty expensive and are generally reserved for urgent matters.
(For example, to call Czechoslovakia from the UK, there is a minimum charge of 13 shillings for three minutes, then 4s 4d for every minute, whole or part after that. This means that you are looking at around £20 in modern money for a five minute call with a decent chance of the secret police listening in...)
As a result, one of the main means of sending messages across borders is the telegram, the 1960s equivalent of the text message. While well down from its 1930s peak, the British General Post Office (GPO) is dealing with around 10 million a year. These can be sent from post offices, many railway stations or even via requesting one over the telephone. They can be sent for a passenger on a flight or a train, to a hotel or to a house; you can even arrange for a telegram to be sent to a telephone number i.e. the operator will ring up the person with the message. Basically, any 'known location' - although you may well have to wait a few hours for the message to reach someone.
These can be used for all sorts of purposes - making hotel reservations for example.
Telegrams are charged per word with a minimum charge, you don't have to write out STOP any more and a whole bunch of commercial codes are available to make your message shorter. In Europe, there is a slower 'European Letter Telegram' which will be posted in the destination country instead of sent on by messenger.
(UK to Czechoslovakia - an ordinary telegram is 5s 3d for 7 words.)
For more real time communication, the Teletype or Telex system allows for communications between machines linked to the international network - you can either hold a real time conversation between two machines as with the recently installed US-USSR 'Hot Line' or prepare your message in advance and send it all at once.
It is even possible to send photographs or copies of documents by telegram (
https://youtu.be/UsdWZKLjLvc) but this is seriously expensive and not the thing that your ordinary person would do - more for governments or news organisations.