In early- to mid-June, you are likely to start noticing purple bird droppings everywhere. You will also see a select group of people in-the-know with telltale purple stains on their fingertips. The culprit: mulberries.
Both species of mulberries are edible, and they're hard to confuse with anything else: there aren't any other local trees bearing fruit that looks like this. The berries look like blackberries, but those grow on canes coming out of the ground, not on tree branches, and they won't come until later in the summer.
In fact, one good way to spot a tree with ripe mulberries is that the fruit will start falling to the ground: if you see purple spots on the sidewalk or street, look up and you're likely to see fruit on the branches as well. This tendency of the fruit to fall when ripe leads to an easy way to harvest large quantities: put a tarp or a sheet on the ground and shake the branches over it. You'll have to sort through the assorted bits and pieces that fall down, but it's still much faster than picking individual berries.
In the wild: Actually, you're most likely to spot this tree in residential neighborhoods, especially along fences where birds have sat after eating mulberries. Most homeowners will be more than happy to have you take some of their berries before they fall on the ground and make a mess. There are some along the paved path in the Peirce Mill area of Rock Creek Park.
In your yard: Because of the aforementioned mess of dropping fruits, most homeowners avoid planting this tree. On the other hand, you and the birds will both be well-fed, and they grow like weeds. The native morus rubra grows to about 40 to 70 feet, so make sure you have enough space before planting.