What happens if you exchange a Honda car and drive away?

I'm curious, what exactly transpires when one decides to trade in their Honda vehicle and take to the roads with a new set of wheels? Do they simply relinquish ownership of the Honda and immediately gain possession of the new vehicle, or is there a more intricate process involved? Are there any legal implications or financial considerations that one must be aware of before making such an exchange? And what about the logistics of the actual swap - how does one ensure a smooth transition from one car to the next?