Wikipedia presents the following information on the Phantom Zone:
The Phantom Zone is a fictional prison dimension featured in the Superman comic books and related media published by DC Comics. It first appeared in Adventure Comics #283 (April 1961), and was created by Robert Bernstein and George Papp
Ah, but as I have discussed in the past, Mort Weisinger and his writers often swiped ideas and entire plotlines from earlier stories and so it is with the Phantom Zone. The precursor to the Zone first appears in Action #131 (April 1949), a full 12 years before its official debut. Here's the cover:
As you can see, the original machine was quite cumbersome, but the effect is clearly the same. The person's color fades, then becomes white (for the benefit of the reader, as the stories always made it clear that the characters in the zone were actually invisible).
In the Action #131 story, Luthor has come up with a new invention:
A teleportation device, in other words. But, in typical comic book criminal fashion the commercial applications for his machine don't occur to Luthor. Never mind that he could instantly put out of business every trucking, railroad and airline company, Luthor's bright idea is to put it to use robbing banks.
In the Silver Age tale, Superboy discovers the Phantom Zone projector (initially called the Punishment Machine) in a box of forbidden weapons that Jor-El had shot into space. He is accidentally sent into the Zone when a lizard presses the button as he stands in front of the projector.
In the Golden Age, Superman is holding a receiver when Luthor's teleportation device signals it. The crook thinks quickly:
In the stories, Superboy and Superman are unable to touch anything in the physical world, or communicate directly with anyone. But there is an indirect method of communication in both stories, and it is the same each time:
Incidentally, that bit with phantoms communicating via an electric typewriter was used at least once more that I'm aware of. Lois let Perry, Jimmy and Clark know she was still alive in Superman #129's The Ghost of Lois Lane:
Update: Commander Benson drops by in the comments and notes a very similar theme in the Atom Man vs Superman serial from 1950. Note particularly Chapter 8, which has Superman sent by Luthor into the "Empty Doom" where he exists solely as a phantom, and where his only means of communication with the corporeal world is... you guessed it, via an electric typewriter. From what I've been able to observe of the serial, it's largely based on the story from Action #131.