A Cuban spy was once arrested that allegedly used a numbers station to receive instructions:
https://en.wikipedia.org/wiki/Numbers_station#Atenci.C3.B3n_spy_case... reminds me 'one time pad'
Yup it's a one time pad. The spy would have a secret key hidden somewhere (there was once a rumour that a spy had been caught with one of these keys hidden inside a bar of soap, and another which had written the key on a stick of chewing gum which would be chewed after the message was received). They would then get a shortwave radio (these were more common before mass produced FM radio's, most radios could pick up shortwave), paper and pen, and tune into the number station at a specific time. They would then write down the numbers given out and decrypt the message using the key and a simple system such as a OTP.
Shortwave was used instead of AM/FM as it can be broadcast much further and the frequency range is less regulated. None of the numbers stations followed any regulations.
This system was chosen because the items are not suspicious, everyone had a pen, paper and a radio. And while it is possible to track the transmittor of a numbers station, It is also impossible to track radios listening in to it. The downfalls of it are that the key can only be used once, it does not allow for two way communication, and only a small amount of information can be transmitted.
It is a very simple system and works very well which is why it still has some use today. Though other systems are also in place.
This is my favourite number station, The Lincolnshire Poacher, which I could sometimes pick up as a kid:
https://www.youtube.com/watch?v=QnXPqUU6fI0This number station was being broadcast from a UK military base in Cyprus, though it is likely to have moved a few times:
http://www.numbers-stations.com/E03/It was shutdown in 2008 and the communications seemed to have been carried by Cherry Ripe instead, as that numbers station format changed to one similar to E03 (Lincolnshire Poacher) after that.
The jingle at the start is a calling code used on sw communications. The first few numbers that are repeated is the ID of the secret key, and the rest of the numbers are the ciphertext.
These communications are impossible to crack without the key (provided they are using a OTP and not reusing keys or generating non-random keys), and the secret key is destroyed after the message is received.
The 'attencion' number station which the Cuban spy used made a few mistakes. First it didn't use OTP, but some other system which required a laptop to decrypt. The big issue was that when messages were garbled, they were transmitted again, but they made a mistake in how they did this (likely reusing the key with a different message) which allowed the US government to decrypt the messages.
There were also Russian number stations which made the mistake of not broadcasting on a set schedule. When the crisis in Ukraine started kicking off, these number stations went crazy sending out tons of broadcasts, letting listeners know that something big was going on.
