The best thing is to have the gun unloaded and locked in a case inaccessible to the people in the car (preferably the trunk, other places will do). Ammo is locked separately.
I don't recommend carrying on your person anywhere you don't have a permit. The FOPA does NOT cover carrying guns on the person; it was intended mainly for competition shooters to transport their target guns. If you are going to carry anyhow, then I agree with Frontgate1; just do it and hope you don't get caught.
The best way to avoid problems is still not to be stopped. So don't drive a red sports car at 105 mph through a school zone, waving your gun and yelling for the cops to "get me if you can."
Seriously, move with traffic, use signals when changing lanes, don't run stop signs or red lights, have an inconspicuous car, no provocative bumper stickers.
And not only keep the gun(s) and ammo locked away and out of sight, but keep gun stuff (speed loaders, extra magazines, copies of "Guns & Ammo") out of sight as well.
How often have you been stopped in your home state in the last, say, five years? If the answer is none, you probably will have no trouble in another state.
Jim