Go to Megaton, and find Mr. Burke.

He will offer the mission to detonate the bomb in the centre of Megaton.

Decline this and tell about Mr. Burke to Lucas Simms. He will go to arrest Mr. Burke.

When he gets killed, loot his (Sherriff's) body and take Armory key.

Then you can enter the armory, but in it it's a powerful robotic guard.

Kill the guard, and you will have asccess to all weapons!