Shallots are generally available year-round, but prime time is from April through August. When selecting shallots, think onions. The shallots should be firm and heavy for their size, not dry and light, and should have no soft spots. Sprouting shallots are an indication of age and should be avoided. The younger (smaller) the shallot, the milder the taste. Large shallots will smell and taste more like their onion and garlic cousins.
Most cooks buy only as many shallots as they will need for a particular recipe, but if you have an abundance of shallots, store them as you would any allium in a cool, dry, dark place with plenty of air circulation. Knot them in clean pantyhose, hang from the ceiling in a dry garage, cellar or closet, and they can last up to 2 months. Or store in a hanging metal mesh basket. If they sprout, you can still use them. Remove the bitter green sprouts if you don't want a strong onion flavor. Many cooks choose to include the sprouts and use them much like chives.
Shallots may be chopped and frozen up to 3 months. However, when thawed, they will have the texture of a lightly sauteed shallot, so do not expect any crunch. This may actually be a time-saver in many recipes.