A few of these cone-shaped, sponge-textured fungi add a lot to pastas and risottos (such as this Morel Mushroom Risotto). If you're lucky enough to have a lot of morels, they are at their finest when cooked quickly in butter and lightly salted (see How to Saute Morels for specifics).
Morels are particularly delicious when paired with those fellow harbingers of spring, asparagus - Asparagus & Morels is one of my favorite things to eat when they're both at the market.
Morels are usually between two and four inches long, and range in color from pale cream to almost black. The darker the color of the morel, the smokier, nuttier, and earthier the flavor will be. Look for fresh, plump specimens whose cut end isn't completely dried out. Avoid bruised or softening morels, since that damage will make them rot quickly.
Store morels in a paper bag and use as quickly as possible. Time in the fridge is just going to dry them out, but if you do need to store them do so in a paper bag so they can breathe, not a plastic one.
Morels need a bit more cleaning than other mushrooms. Shake them clean, swish them in cold water, lift them out and dry (for more specifics see How to Clean Morels). Don't clean morels until you are ready to cook them, since they will have absorbed some water and are more likely to mold or rot if stored after cleaning.
If you're lucky enough to get a lot of morels, you can always dry them.
Like all mushrooms, morels have deadly imitators. If you decide to try foraging them for yourself, do so with an experienced guide. Mycological societies around the country offer free mushrooms walks and mushroom identification seminars.