CIn reciprocating engines, it's just a matter of ensuring the fuel pump is on and the mixture is open. Restart is simply a matter of turning the key at that point and the power comes back almost instantaneously.
If you used the mag switch (what I assume you're referring to as the key) to shut the engine off you're probably going to have a very rude awakening when you turn the ignition back on….little things like exhaust manifolds be cracked or separated, engine fire, etc. Ever going roaring down the road and shut the switch off in your car then switch it back on?
Another problem that could pop up would be a runaway prop on restart. These are quite stimulating.
In a general aviation light piston airplane it is a pretty simple thing to do an air restart. With the bigger, higher performance engines used in combat aircraft it just isn't quite as simple all the time.