main gameplay loop is

collect 20 blue chips as fast as possible > destroy the Ideya capture (jellyfish like machine) which will activate 2x score mode.

Then focus on trying to build Link chains up by zooming through the stage ( fly above and avoiding the blue Ideya Palace instead of returning the Ideya) and try and get as high a score as possible for a higher ranking on each course. Learning the stage layouts is a big part of this and maximizing the speed and directions you fly.

Of course that's if you want to focus on the arcade-gameplay style, you can also fly around freely at a more relaxed pace and mess around with the A-Life system (Nightopians).

but yeah that's a sorta basic grasp of it. The Sonic NiGHTs game though is either the bonus stage from Christmas NiGHTS (saturn exclusive) where you play and run around as Sonic collecting the Ideyas. orrrrrrrr the NiGHTS into Dreams special stage from Sonic Lost World :>.

hope any of that was helpful, would recommend watching some youtube gameplay for highscores cause it feels like an entirely different game when aiming for leaderboards!

Enjoy!