All those colored squares are players in a spaceship. At the bottom center of the screen you see the hotbar. Those are modules fitted to the ship. You can double click in space and your ship will head in that direction (manual flying), or right click an object or player in space and follow them, orbit them, so on. Then you activate your modules and manage your recharging energy.
The game mostly plays by outfitting your ship, right clicking and telling your ship what to do (jump through stargate, warp to, orbit, approach, keep at distance), and then activating modules (guns, defenses, repairs, propulsion mods and so on). What makes the game insane is a lot of good systems like the free market, construction of assets and the groups of players interacting with each other to create an incredibly dense meta game.