As stated in the title, what is the easiest way to reach to Dongzhimen Metro station from Beijing Capital Airport (PEK)?
Take the Beijing Subway Airport Express Line (北京地铁机场线). It goes right from Dongzhimen to PEK with only one stop in between.
There are two stations at PEK, one in Terminal 2 and one in Terminal 3. The Airport Express costs ￥25 per trip, for which you could either use a Beijing public transportation card or buy a single-trip ticket at a vending machine, located in the Dongzhimen station.