Symmetrical is a bit more complicated, as it need a pole and topping lift for the pole. Sym allows you to sail dead downwind.
Asym is easier. Think of it as a symmetrical with the pole all the way forward to the forestay. So, just stick the pole out the front of the boat all the time. The asym is sailed more like a big genoa. There are different shapes - the flatter it gets, the closer to the wind it could sail. Asyms do not sail dead downwind, because they would get blanketed by the main. I believe some try to sail an asym wing on wing, but the asym is less of a drag type of sail, and designed to sail higher angles, maybe down to a deep reach, while still developing lift. This way, they are faster and hence the ideal of "hotter" angles.
Asyms are pretty easy to deal with. Some use a sock, but I don't. You can always turn DDW and blanket the asym with the main to take down and hoist. Gybing is much easier, because you don't have to bother moving the pole as you do on a symmetrical. I think for this reason they have become favored in cruising circles.
On our narrow lake which runs roughly east/west, we mostly get westerly winds. This introduces the idea of "short gybing," just the opposite of short tacking. I play with the asym like this, but it really would be much better to set course on a deep reach with the asym drawing and hold for a long period of time, rather than trying to gybe often. For that reason, I seem to sail in lighter winds just as fast if I pole out my jib and go DDW wing on wing. That being said, we have a few portsmouth racers who race solo, and set symmetricals solo. One was a J/24 the other is an Impulse 21.