How did DC become the nations capitol?

DC did not become the nation's capitol. Washington D.C. did.

The location for the national capitol was the result of a compromise after the Constitutional Convention. The Northern and Southern states disagreed about where to locate the capital. The Northern states wanted it in the north, while the southern states wanted it in the south. Eventually, they reached a compromise and decided to create a new city on land donated by Maryland and Virginia. This new city would become Washington, D.C., and it would be the capital of the United States.