You kennel the dog and tie down the kennel to metal D rings that are attached to the vehicle. Now you know how to safely transport a dog!

https://gunner.com/blogs/pack/why-should-i-tie-down-my-dog-c...

There are also various harnesses that attach to seatbelts for non-kennel transportation.

https://www.chewy.com/b/car-safety-11554

The dog wears a harness, and a strap clips into the buckle seat and onto the harness. When you get where you're going, you unclip the strap from the harness, clip on the leash, and off you go.

Weird, I've lived with dogs my whole life but have never heard of anyone doing that. Must be cultural.

Dog harnesses that attach to seat belts are sold at most pet supply stores in the US. There are also short leash like tethers they connect to seat belts and hook to a typical walking harness.