They will spin the upper stage, and release them a few at a time, then spin it up faster, and release more. Source.
In order to save mass, each of the 60 satellites will not have its own release mechanism, such as a spring. Instead, Musk explained, the Falcon rocket's upper stage will begin a very slow rotation, and each of the satellites will be released in turn with a different amount of rotational inertia.
"It will almost seem like spreading a deck of cards on a table," Musk said. There may actually be some contact between the Starlink satellites, he added, but they are designed to handle it.