There are more than two types of rotary shaft tachometers, some digital and some analog in nature. The simplest digital tachometer
sensor is any device that produces one or more pulses per shaft revolution. A typical analog sensor produces a voltage that is proportional to shaft rotation rate and is mechanically coupled to the shaft. Analog sensors are ancient history and are seldom specified for new designs.
You need to decide what type of digital sensor you are going to use to interface to your Arduino. For relatively slow shaft speeds this could be something as simple as a magnetic reed switch that is actuated by a permanent magnet attached to the shaft. Two magnets attached to the shaft opposite each other would be better to maintain dynamic balance, but this type of sensor has a low maximum speed because of limitations on how fast the magnetic reed switch can operate. A inductive pick-up coil can be used in place of the magnetic reed switch for higher revolution rates, but the output is a series of bi-polar pulses whose amplitude is a function of shaft speed. These pulses would normally be conditioned by electronics to produce pulses of uniform amplitude and pulse width for counting and timing by the Arduino as described by
@AnalogKid in post #3 above.
I have recently used
Hall-effect magnetic sensors to measure shaft rotation speed on a mechanical vacuum pump, using a missing-pulse detector circuit to determine when the shaft is no longer rotating because of motor or drive belt failure. These come in two types, one with a built-in magnet for sensing ferromagnetic objects (like the steel spokes on my vacuum pump pulley) and one without a built-in magnet that requires an external magnet to actuate it. They are very reliable and easy to interface to an Arduino.
My favorite inexpensive digital sensor is a retro-reflective optical sensor. This is a light emitter, typically an infrared LED, adjacent to a photo-transistor or photo-diode. and usually in the same package. Optics built into the emitter and detector provide a sensing range on the order of a few millimeters. A contrasting reflecting tape is applied to the shaft to produce an output when it is aligned with the emitter/detector pair. Again, signal conditioning electronics is required to produce pulses of uniform amplitude and suitable logic levels for counting and timing by the Arduino. One small disadvantage of the retro-reflective optical sensor is possible sensitivity to, and interference by, ambient light sources, unless a shroud is used to exclude ambient light.
There are numerous commercial devices available that will provide 0 to +5 volt pulses that can be processed by the Arduino. I would suggest you do a Google search to find something suitable to your purpose and then come back here for help (if you need it) on how to program the Arduino to measure shaft rate from multiple sensors. That is a non-trivial task for a single Arduino sketch, but you could use one Arduino for each sensor and that would be a "piece of cake" to program. An
Arduino Nano is a suitable candidate here and they are "dirt cheap".