There are two major grocery stores serving Shaw. There is the Giant between O and P Streets on 8th Street, NW. The second major store is the Whole Foods (aka Fresh Fields) on P Street, between 14th and 15th Streets. There are various mom & pop stores throughout the Shaw area providing milk and other products.
The Giant Supermarket has fresh vegetables, a fish counter, a wine aisle, pharamacy, bakery, and deli. Their customer service desk provides Westen Union services, bus and other WMATA passes, lottery tickets and check cashing. It is a 24 hour store, with some limited hours on Sunday and holidays. Busy times are usually noonish, and after work, lines during this time are long and confusing. If you can shop between 7-9 am, 2-4 pm, or after 9 pm, do so to avoid the confusion.
The Whole Foods Market has a fresher and more expensive selection of products. The store has a mix of organic and conventionally raised produce. It also has a seafood counter, a meat counter, a cheese counter, sushi counter, deli counter, wine aisle, hot food counter, and Jamba Juice bar. Like the Giant, it has busy hours where lines are long and confusing. Shop early in the morning to avoid the crowds.
Where ever you are in Shaw there should be some little market in a two block radius that sells milk, toilet paper, and other sundry items. They may or may not sell a liquor as well.