I recently made use of both the 24 hour and 144 hour transit visa. Have your paperwork ready which means for the 144 hour--a copy of your ongoing flight to another country and your hotel reservation. Upon arrival in Bejing's Terminal 2 the Transit Visa desk is right next to the general visa line. Just stop off there and get your 144 hour transit visa added to your passport and then join the regular thong pass through the visa approval. (Note I was expecting a 72 hour visa but they gave me the 144 hour one).
Flying into Terminal 3 and transferring to Terminal 2 was more complicated. Here you need the 24 hour TWOV just to get out of the airport. Unfortunately the TWOV's desk at Terminal 3 is harder to find especially depending on which gates you came from. Several others had the same problem as the signage doesn't make sense and the directions we were given didn't either. The TWOV desk is either before you reach the general visa que or after it depending on which direction you are coming from. In my case it was after the que and one had to go through the health screen sensors which put us a couple of hundred feet past the general visa que. Once there you just need to show your outbound flight, receive a stamp in your passport, go back through the regular visa que and collect your luggage and catch the free bus to your next terminal.