If I live in Georgia and my wife lives in DC, how do I go by divorcing her since we've been separated for 2 years?

If you have been a resident of the state of Georgia for at least six months, then the state of Georgia has jurisdiction over your status as either married or not married. Whether the state of Georgia has any jurisdiction over the person of your spouse is another question. If she will voluntarily signed papers and submit herself to the jurisdiction of the court, you can have an uncontested divorce in Georgia. You can also have an uncontested divorce and the state of her residence as well as a contested case in the state of her residence. You may or may not be able to have a contested divorce in Georgia depending on whether there is jurisdiction over her person.