How do you shift gears in a manual car for the fastest acceleration?

You should shift to keep the engine RPMS as close to max horsepower output as possible. I.E. If your car has a redline of 8,000rpm and makes 250hp max at 7,200rpm. If you have gears that make a 1000rpm difference between each shift and you had a completely smooth powerband, then you would shift at 7,700rpm, because any higher and the engine is producing less power than the next gear would provide. Hope that helped, its a hard subject to explain without physically showing you on a dyno.