1. Increasing Engine Power: The engine is the heart of acceleration. By increasing the amount of fuel burned (and air taken in) or by adjusting the engine's internal workings, the engine can produce more power, which translates to faster acceleration. Think of pressing the gas pedal harder.
2. Improving Traction: For the engine's power to translate into forward motion, the car needs to grip the road. This is where tires come in. Better tires with more tread, or a surface with more grip (dry pavement vs. ice), will allow the car to accelerate faster.
3. Reducing Resistance: Anything that resists the car's forward motion will slow it down, making acceleration slower. This includes factors like air resistance (think drag), friction from the tires and engine, and even the weight of the car itself. Reducing these resistances, perhaps by streamlining the car or reducing its load, will improve acceleration.