Per this concept art (from the original studio designer for Predator 2, Crash McCreery) it appears that the first "smart-disc" was activated by compressing the two parts together and steered using the Predator's targeting laser.
In later films and games, additional functionality has been added such as emergent blades, nano-molecular chainsaw edges and sharpened teeth. These are described as being mentally controlled (often by Predators who've earned the rank of "Disc Master"). As such it seems likely that they're activated using the same mental techniques.