This year Washington DC hosts the National Cherry Blossom Festival from March 31 to April 15. Fortunately, the cherry blossoms are expected to be at peak bloom during the first week of the festival (April 1 to April 7). If you're going to see the blossoms for the first time, here's my advice: Take Metro. There won't be a parking space anywhere near the Tidal Basin and the sheer number of pedestrians will make traffic horrendous.
Now's a great time to buy cherry blossom t-shirts to wear to the festival.
Cherry Blossoms White T-Shirt