How do we get to Super 8 Hotel Deng Shi Kou from T2 Beijing Capital Int'l Airport and vice versa?

For your arrival, do you mean you arrive at 12:05 at noon? If so, you can take the airport shuttle bus line 3 to reach Chaoyangmen Station and then change to take a taxi to reach your hotel directly.
At that time to reach the airport, there is no shuttle bus, so the best method is to take a taxi to reach there directly.

Thank you, Hank, for your reply. However, we will be arriving in Beijing at 12:05 a.m. (5 minutes past midnight).

If you reach the airport at midnight, you can take the airport shuttle bus line 2 to reach its terminal and then change to take a taxi to reach your hotel directly.

Again, thank you, Hank, for your reply. I really appreciate it. :D

after 12 midnight there will be no bus. You must take the taxi to your hotel, Bring a printout of the map and chinese translation with telephone number of the hotel so that the driver can find it. We had a similar experience but still had a hard time finding our hotel, going back you could take metro to dongzhimen station to take the airport express train, but if you are carrying luggage and more then 2 person in your group you should take the taxi going to airport. Then show number 2 sign with your finger he will know that it means terminal 2

Thank you, Mr. Quazar, for the instructions. That's also how I understood it at first-- i.e., there'd be no buses after midnight and that the next trip of the bus from Terminal 2 would be at 6:35 a.m.

I will have to seek help from contacts regarding Chinese translation of the hotel's address. It's not available online (sigh!) and it's quite unfortunate for us that we have no way of contacting either the hotel or the "agent" with whom we booked our hotel except through overseas call from the Philippines. Can't believe that they don't have inbound email address!

Anyway, thank you again for taking time in giving us your valuable tips. It gives us a glimpse of what to expect then.