If you're prepared to take a chance on what you might get to see, half-price and discounted tickets are sold to personal callers, on the day of the performance, at the TKTS booth in Leicester Square. (It's the ONLY 'official' outlet for such tickets within central London, but there's another branch at Brent Cross. It's run by the Society of London Theatre, which represents all of London's theatres):
http://www.officiallondontheatre.co.uk/tkts/
For advance booking, you should always go through the agency appointed by the theatre or the company behind the show. (It's usually Ticketmaster, but not always).
Start here:
http://www.officiallo...e.co.uk/london_shows/
The links from those pages will take you to the website of the show, or of the theatre. Then you click on the 'Booking' link there, confident in the knowledge that you're being directed to the OFFICIAL sales outlet (and not to one of dozens of other agencies, which might not be trustworthy or reliable).
Chris