There are two main ways of producing instant coffee - freeze drying and spray drying.

In freeze-drying, brewed coffee is frozen into granules, which are then placed in vacuum chamber, where the water sublimates (evaporates w/o liquifaction).

In spray-drying, brewed coffee is sprayed in tower and dried by hot air in the matter of seconds.

Freeze dried instant coffee advantage: higher quality product, better preserved flavor.

Spray dried instant coffee advantages: faster and cheaper.

Source:
Producing Instant coffee