What is the best way to get from Beijing south train station to Beijing capital airport and cost?

You could take a taxi to Xidan station first and then take the airport bus to Capital airport. Or, you can take subway line 4 to Xuanwumen Station, then to Dongzhimen Station by subway line 2 and last to Capital airport by the airport express rail. By subway, it costs less, which is around CNY30 per person.