What subway lines should I take from the Beijing Airport to the Jade International Hostel.

No direct subway can take you for this journey. I suggest you take shuttle bus line 2 to Yonghegong Lama Temple Station, where you can transfer to subway line 5 to Dengshikou MTR Station. Get out from Exit A, you can walk about 1.2km to your hotel then by asking the local people about the exact location. Or a taxi can take you there in about 5min then.

you can take shuttle bus line 2 to Yonghegong Lama Temple Station, and then transfering to subway line 5 to Dengshikou MTR Station. Get out from Exit A, you will see the hotel.