Every five minutes it's not being played, it generates a dream cloud. Some of these clouds contain pokemon or items, but other than that you use the laser to break clouds and get dream orbs, which can be spent on upgrades to your laser and visor, or used to buy items to help catch pokemon.
When you reveal a pokemon/item, it enters a catching minigame where you need to hit the rapidly moving orb to stun it, then mash A to fill a bar. When it's full you catch it, and if you don't get it on time it gets away.
I don't know how the legendaries work; I've had Tornadus fly across my screen once, but I think that was part of a cutscene.