Run by the Society of London Theatre, the TKTS booths in Leicester Square or at the Canary Wharf DLR stations are the ONLY places to get real half-price theatre tickets for the same day. The other places lining Leicester Square will happily sell you an upper balcony ticket for half the price of an orchestra seat. Make sure you go to the right one and don't get duped!
I've only purchased from the one in Leicester Square, mainly because Canary Wharf was out of the way (although fairly convenient if you're coming back from Greenwich), but they offer the same shows.
In order to find Leicester Square booth, come out of the Leicester Square Tube station and walk towards the square. After about a 5-minute walk, you'll see the garden. The booth should be to your left, in the garden facing the Odeon movie theater.
The five times I went there, there weren't more than five people in line. Before you get in line (or while you're in line), take a look at the bulletin board and decide what you want to watch.
Usually the seats available are orchestra seats with unobstructed views. I went to Phantom of the Opera, Stomp, and Les Miserables and got central seats in the first five rows by buying my tickets before noon. You don't get to choose your seats, but from my experience, it's not a problem.
If you're a theatre fan, you can definitely get your money's worth. However, not all shows are available all days. And the very new/popular ones won't be available. Check the website to get an idea of what's playing.
Website: http://www.officiallondontheatre.co.uk/tkts