What is the best way to get from the Beijing Airport to the Ritz Carlton Financial District?

The beste way is taking the airport shuttle bus line 2 to reach Xidan and then take a taxi to reach that district.
If you want to take the express train, you can take line 2 at Dongzhimen Station to reach Fuchengmen Station. Then you can walk along Fuchengmen Inner Street to reach Taipingqiao Street. Then you can walk along Taipingqiao Street to reach that area directly.