Once you track down mulberries in the wild or at the market, keep in mind that mulberries spoil quickly. Use them immediately (or refrigerate for a couple of days) - make sure you pick or cut off the stems first. If keeping them longer, freeze them. To freeze, wash and pick over, dry gently, and place on cookie sheet in freezer until hard. Then pack loosely in container for later use (note that the berries may be mushy when thawed).
I just ate a whole bunch raw and found them mild in taste and a little sweet-bitter. They are really fragile and picking off the stems led to red fingertips very quickly. I took to them with my kitchen shears, but honestly I don't think the stems really get in the way too much if you happen to eat them. I also added a few to a glass of vinho verde along with a sprig of fresh mint (also from my CSA bag). The rest are on a cookie sheet in the freezer getting ready for another use...
Other ideas for mulberries:
• Toss them into muffin batter for tasty, seasonal muffins
• Use them in place of blackberries or raspberries in your favorite cobbler or pie recipe
• Mash them with a sprinkling of sugar to add some sweetness and use this syrup on ice cream or as a topping for pound cake or yogurt
• Toss fresh berries into sangria, vodka tonic, or lemonade for a seasonal pick-me-up (great use for frozen berries - it'll keep the drink cool while it adds flavor)
• Or mash them with some fresh herbs (rosemary would be good) into a chutney to serve with local cheese and fresh bread for a summertime appetizer