3-wire fans will work fine. The 4-wire system is just a different way to control speeds that came after 3-wire, and the connector and BIOS designs were made backwards compatible. If you look closely at the connectors, you will see that there is only one way to put them together. It is set up so that a 3-wire fan can plug into a 4-pin mobo header only one way, with the 3 wires connected to the correct pins.
A 3-wire system uses those 3 for Ground, +12 VDC (controlled) supply, and fan tachometer signal. The tach signal simply feeds the mobo 2 pulses per fan revolution so it can measure the fan speed. In the case of a CPU cooler fan, based on a temperature probe built into the CPU the mobo changes the DC voltage provided on the +12 VDC line to change fan speed and maintain proper CPU temperature. There is no connection to the fourth pin on the mobo pinout connector.
In a 4-wire system, that controlled variable DC voltage supply is not used. Instead, a fourth wire supplies to the fan a rapidly-pulsed signal that provides control by Pulse Width Modulation. It's just a different way to vary the average voltage supplied (and hence the fan speed), but it has some advantages for low-speed operation.
Either way, IF you set the mobo to control the fan speed (default setting), it monitors the temperature inside the CPU case with a temperature sensor and varies the power supplied to the CPU fan to keep it near the temperature setpoint via a simple feedback control loop. As an additional function it monitors the actual fan speed which it can show you, plus it uses that fan speed to detect an emergency situation if the fan suddenly stops turning. In that case, no fan speed is a warning to shut things down and prevent CPU overheating, and this will likely be recognized and action taken before the measured temperature starts to rise quickly.
For case fans, a similar system is used, except that the temperature input for the feedback control loop is a sensor on the mobo somewhere, rather than inside the CPU.