Or buy a $1 module from Ebay that drives the 7-seg display with commands from the SPI or I2C bus.
e.g. MAX7219 or TM1638
Yes, the driver chips handle the multiplexing.
You can use bare 7-segs and look after the multiplexing with an Arduino interrupt routine.
If your Arduino crashes or you disable interrupts, you burn out the LEDs that are currently lit.
The custom driver chips do not have this problem.
David.