Usual tips for arriving at TBIT, & repeating some things already said.
When you deplane, go as fast as you feel comfortable to do to reach the immigration hall; mine is a pretty fast walk and I care not about what the people I overtake think of me. It can be quite a long distance, and anyone you overtake will probably save you time through immigration. My personal best time from exiting the plane (J) to outside the terminal is 15 minutes; that had minimal queuing time and my bag was waiting for me at the carousel. If you are unlucky with queues, it can take 30 minutes or more.
When you reach the immigration hall, most likely there will be a number of queues already formed, starting at the point where you enter the hall. Don't automatically join the first or second queue you reach, unless they are short (say 5 people). Each queue is usually serviced by 2 immigration officers; sometimes 3, sometimes only 1. Keep walking and there are usually shorter queues a bit further along. Make sure you join a 'foreigners' queue (unless directed otherwise).
You'll be electronically fingerprinted and have your picture taken.
J and F bags come out on a separate carousel (usually to the left as you walk away from immigration) and they are usually there, or starting by the time you reach the carousel. Note: some-one is there taking at least J and F bags off the carousel as they appear, so if bags are on the ground when you get there, check them as yours may already be there and you'll wait forever watching the carousel!
Reclaim bags, then its queue again for customs, usually 2, one in the middle and one to the left. The LH queue tends to be shorter, but is also accessed by crew and ?VIPs? so you can get delayed there. Usual queue lottery!
After customs, bear right up the ramp to drop your bags off (no doubt tagged all the way through), then after a few steps you are out of the terminal. HOWEVER I note serfty mentions 'transit security' above and I'm not sure what he means by that (he knows the TBIT system well). I'm not aware of any security other than what I mention below, but I stand to be corrected by serfty.
If you come out the 'usual' door to the outside, go hard right immediately and there should be a staircase taking you back up to the departures level, where you enter and walk forward, past the check-in counters to the RH back of the check-in hall where you'll find entrance to departure security. Its strict, so be prepared. ALL shoes off (even if 'plane friendly' type); completely empty your pockets of EVERYTHING as you will almost certainly have a body scan. Again, timing can be 5 minutes through departure security if you are lucky or 15 mins (or, of course, more).
Then up to the lounge via the lift almost dead ahead when you exit security and apply for a shower.
Good luck!
