Onions come in bulbs, these are called sets, and they're the easiest way of onion planting. You can also plant onions in the form of transplants and seeds, but most gardeners prefer using sets.
Onions should be more than ready for you to harvest them in early summer if you planted them in the fall, while spring-planted onions are usually ready for the harvest in early fall.
Onions aren't prone to illnesses, but can easily contract pest. The Onion Fly, for example, is an insect that will lay eggs around the base of the onion where the larvae of the fly will hatch.
Plant them as soon as the frost lets up and allows you to work on the soil. When you have to decide do you plant onions in the fall or spring, remember that the harvest in the spring is definitely going to be plentiful.