There is direct bus running from Tianjin airport to Tianjin railway station. You can take it. The cost is CNY10.
There will be land signs leading to find the platform to take bullet train to Beijing at the train station. You will stop at Beijing South Railway station. The hotel is next to Chongwenmen station, thus you can take subway line 4 to Xuanwumen from the train station and then take usbway line 2 to Chongwenmen station. You will find the hotel when get out of the station