Contrary to popular belief, it is possible to wash wool garments with the aid of your washing machine. However, certain precautions must be taken to do so successfully. Wool's biggest enemies in a washing machine are agitation and unwanted stretching, so you will have to take care to avoid both of these things.
Soap choice, as you might imagine, makes a big difference when washing wool. Your normal washing powder, no matter what it is, is a poor choice, because all laundry detergents are too alkaline in nature for the delicate character of wool. This includes Woolite. It is useful to remember that wool is actually the hair of a sheep, and, much like your own hair, demands special treatment.
When washing wool, a far better choice is Dawn dish soap. If possible, the yellow or blue kinds seem to fare better than the others. If you cannot locate Dawn, you may try another dish soap that you like. However, as San Francisco fibre arts scene fixture Fuzzy Galore points out, Dawn is the soap of choice used when ducks and other water fowl happen to wander through oil slicks. If it is good enough to clean oil yet gentle enough to not harm a duck's feathers, it should be good enough for your wool garments.
Agitation is the number one cause of fulling and felting of wool. If you do fibre arts of any kind, you may have heard of felting. Felting simply means that natural fibres have been exposed to moisture and agitation, and so have become matted together to form a solid piece of fabric. Fulling is similar, only it's a process somewhere in between your normal, knit wool garment and a felted one. If you have ever shrunk a wool sweater by accident, but it and its stitches are still recognisable, you have fulled a sweater.
To avoid either unhappy instance, use a top-loading washing machine. You will want to use the rinse and spin cycle, so it is important to be able to access them directly and avoid having to go through the normal wash cycle just to get to those two cycles at the end.
Washing and Drying
Let the machine fill with water, then stop it and add 1/4 cup of dishwashing detergent to the water. Following this order will avoid the creation of foam. Put your wool garment on top of the water and allow it to soak the soapy water up. Once it has soaked, remove it from the machine and drain the water. Put the garment back in the machine and set the machine to "spin." This will allow it to drain more water out of the garment than you could by hand, yet it will not agitate the fabric.
Dry the wool by laying it carefully on a fluffy, clean, dry towel on a flat surface, away from pets and children. Try not to stretch it excessively, but definitely guide it into the shape it was originally. Drying can take anywhere from 12 to 72 hours, and you will need to occasionally turn the garment over to make sure all surfaces are allowed a chance to dry thoroughly.
Don't ever stick your wool garments in a clothes dryer unless you are purposely trying to shrink them.