I agree with the previous comment that it's best to start the process early and determine how much you're approved for with a lender. Plus, in the DC area, any offer for property must be accompanied by a mortgage pre-approval letter.
At the same time, you can start working with a real estate agent to start learning about the market and identifying properties that interest you. For example, I have several clients in your position that are planning on moving to DC in the summer/fall. They receive frequent automated searches that meet their budget, location, and other preferences, and we refine the search along the way.
It's a fairly straight-forward process, but the DC market is competitive for buyers right now. So, starting early will only help increase your knowledge of the market. Feel free to contact me with any questions.
TTR Sotheby's International Realty