The clutch is replaced with a torque converter which contains oil. When the engine is accelerated the oil in the converter is thrown outwards againsts vanes which when sufficient force is generated moves the car. when you ease the engine speed the reverse happens until you are stopped. The engine speed at tickover speed is insufficent to drive the vehicle although occassionaly when the oil is cold the car can attempt to move forwards slowly
Citroen used a system called C-matic for years, which had a normal dry plate clutch, but it was activated hydraulically when you moved the gear lever, rather than you having to put your foot on the clutch as well...modern systems are basically a derivative of C-matic.
ford transits had this for a while, proved unreliable thou'.
when you move the gear lever it senses this and dips the clutch. on releasing the lever in the new gear the clutch is reapplied. once you got used to it it was ok . like an auto box but you had to select the next gear.
same as in a normal manual car you have to lift off the throttle as you change.