Find the Museum of Technology
You can ask Three Dog for directions to the Museum of Technology and the Washington Monument. From the radio studio, where you met Three Dog, proceed downstairs to the back door of the Galaxy News Radio building. From there you will need to locate the entrance to the Collapsed Car Tunnel. From the back door of GNR, you can see a bus below and to the right. The entrance is to the right of the bus. You may also notice some Feral Ghouls roaming around the bus. Cross the bridge on the left and turn right to find some loot at the picnic table, then you can jump down onto the bus.
Enter the Collapsed Car Tunnel door and follow the tunnels to Dupont Station. Enter Dupont Station and follow the waypoints south, while staying on the Red Metro line. You will pass the Central Station and then later reach the Museum of Technology. During this trip you will encounter lots of Raiders, Feral Ghouls and a few Super Mutants, so make sure you have plenty of Stimpacks, ammo and weapons
Retrieve the Communication Relay Dish
Inside the Museum of Technology you need to find the Virgo II Lunar Lander, which is located in the West Wing of the building. You can obtain this information from a terminal in the Atrium to the right of the entrance when you come in. Note however that the place is crawling with Super Mutants. Your goal is to reach the West Wing going through the Vault-Tec demonstration vault, upstairs. You can also attempt retrieving Jiggs' Loot using the Museum Information Terminal in the Atrium.
In the West Wing, locate the Virgo II Lunar Lander. The west wing is divided in 3 areas: The Planetarium, the Delta IX Exhibition and the Virgo II Exhibition. Be ready for a fight as all these areas are patrolled in some way by Super Mutants. Beware that you do need either Science of 25 or Lock Picking of 50 to get through the Planetarium. So if you do not have those stats it's recommended that you go through the Delta IX Rocket Exhibit.
Once you've found the Lander and cleared all hostiles, grab the dish by interacting with the Lander and make your way to the exit.
Find the Washington Monument
Exit the Museum and head west for the Washington Monument. It is also in The Mall area and can be seen from the entrance of the Museum of Technology as a giant obelisk. There are Brotherhood guards stationed there and you'll need to use the terminal to open the security doors. The password is given to you in your notes at the beginning of the quest. Take the elevator to the top and interact with the radio equipment to install the dish. Finally, return to Three Dog at Galaxy News Radio to finish the quest.