I was going to recommend taking the three-day Skip Barber open wheel class, but looks like they've switched that to the Mygale Formula 4 cars with a sequential gearbox. When I did it, they were Dodge powered with the old straight-cut gears with dog rings.

I suspect you could find a Formula Dodge or Formula Ford racing series with an intro class if you just want to learn the gearbox aspects, plus then you can learn to rotate a car with the steering wheel, the gas, and the brake pedal. ;)