I've turned a few heads doing this - people can not believe I just put their old grill in my car and drove away. Basically the cookbox comes off and the frame stays together.
My now standard method is to remove the lower wire rack (or wood slat sections) and the drop in work table(s). Then remove cooking grids and flavorizers, remove the knobs, side burner, control panel, and manifold, pull out the burners. Then I brush any loose gunk down into the grease pan and remove the pan. Then I remove the lid, break the cookbox bolt off (often you need to crack off pieces of the plastic washer to get to the head of the bolt - then a 7/16 six point socket breaks it right off). Lift off the cookbox.
The frame then goes into the car in one piece with flip table(s) facing up so they can't flop around while loading. If it's a long frame grill (like a C) I put the passenger seat forward a little. I put the flavorizers and grids carefully into the lid and place in car. The cookbox goes in and the grease pan goes into the cookbox so it can't tip over and spill. Wire rack goes in. All the small parts go into my tool bucket and the other things (manifold, tables, control panel, side burner) all go on the floor between the front and back seats. Of course back seats are folded down. Since I use my Prius more as a truck than a car that heavy cardboard stays in there all the time.
Sounds like a lot of work but I've got it down to 10 minutes or less
Picture below of the blue lid Silver C (a little different loading because the lid had a frozen pin so it went with the cookbox). Other picture is the Cranberry Silver C (note frame is upside down. This is where I learned to load with flip tables UP so they don't interfere with loading).
Yes, I'm at least half nuts