You may have all heard about the half-price ticket booth in Leicester square, London, where one can get the hottest theatre and musical tickets. While this is a great way of acquiring tickets, the show list they have tickets to on a daily basis is limited, and you do have to line up for some time, especially if the tickets you want are the same as what everybody else wants.
Two tips: One, locate the theatre of the show you want to go to, and get to the box office about a few hours before the show. The attendant may tell you to come back an hour or 45 minutes before the show, but at least you can talk to him/her and gauge if there are likely to be any returns of the day (tickets from people that can't make the show after all). This method works best on a weekday.
Two, if you have access to a computer, or an internet cafe nearby, log on to lastminute.com and find tickets for as low as ten pounds.
Of a list of plays and musicals in London, see the Official Guide.