Questions for speedometer moto with arduino

There are different sensors and techniques that can be used, but most rely on measuring the movement of one of the motorcycle's wheels (usually the front, because that is not attached to the motor). The easiest way would be to count the number of full revolutions in a given span of time, then use the circumfrence of the wheel to calculate the speed.

As to what type of sensors are available to do this... Most people would use optical or magnetic sensors to detect when a specific point on the front wheel passes a stationary (relative to the motorcycle as a whole) sensor, usually on one strut connecting the front wheel hub to the handle bars. There are other methods like adding a potentiometer or rotary encoder to the wheel hub, but those are more likely to require significantly more disassembly and modification to the vehicle.