The tanks were transported to the front by rail, and the the crews collected them at a depot. Sometimes, it could take quite awhile. The author of Panzer Gunner spent almost half of 1943 on "guard duty" in Trieste, waiting for his unit's Panzer 4's to arrive.
And you would indeed need to learn the controls. Usually, if a tank was captured, it was damaged, and so would be sent to the salvage units. They would fix them up, put on markings, and sometimes even replace all the labeled parts with German labels (for instance, one of the M3 Greyhounds in a reenacting unit out here is actually a German capture. All american markings and labels were changed to German, including things like speedometers and such. That would all matter on how much time the salvage guys had. Then, if it was deemed acceptable, it would be sent to a panzer unit that needed tanks badly, and could not wait for resupply.