Oh, this is a classic! There's a complete guide to the entire hoax called
Turn Me On, Dead Man by Andru J. Reeve which tells you every single detail, some of which are absolutely beyond crazy. Though it is of course true that if you play "Revolution Nine" from the White Album backwards, you really can hear a spooky voice saying "Turn me on, dead man!" So that totally proves it.
The best "clue" is that if you hold up the Magical Mystery Tour album to a mirror, you can supposedly make out a UK phone number. If you called this up at special times mentioned in the songs, you supposedly got either a recorded admission that yes, Paul really was dead, and you're very clever for figuring it out, or something even more strange, such as a direct line to Heaven so that Paul could tell you in person how dead he was. There were several different numbers you could more or less make out, all of which had to be permanently disconnected because random UK citizens who of course had no connection with the Beatles were getting constantly woken up at 5 AM by stoned Americans who thought they were Paul McCartney's ghost.
And here's an image you may find amusing: