I often tell my clients that my wool garments can easily be washed by hand and in some cases [i.e. my hand-knit hats] they can even be washed in the washing machine on a gentle cycle in cold water and very little detergent [special wool detergent would be best]. But in reality I rarely wash my wool pieces unless I actually manage to stain them which isn't an easy thing to do as any liquid usually pearls off and dirt sits on the surface of the fibers and can easily be wiped off with a damp cloth. The easiest is to air out the garment if necessary. And if you decide to wash it be aware that wet wool has a little bit of a funny smell which is nothing to worry about as it will disappear as soon as the piece is fully dried.
A complete guide on garment care can be found here