I always fancied using a sewing machine foot pedal as an accelerator... Only thing I'm not sure about with those is exactly how they work and what kind of resistance they have...
Perhaps with a small circuit for a psuedo gearbox (so it gives you more of a range of speeds, if you wanted to go slower you could drop a "gear", easier to impliment than a real gearbox but less effective).
Still, a couple of 12/24v batteries and something like that, a couple of motors, some wheels/tires, brakes, steering, you're good to go. It's a really basic plan as far as karts can go, you might not want the motors driven directly by the motors, you might want 2/4 wheel drive, etc, there's a whole bunch of decisions you could make depending on how much you've got to spend and what the kart's for.