Buying tickets online is an easy and effective way to get discounted tickets and gives you more control in getting tickets to the shows you want to see opposed to getting discounted seats at a Leicester Square ticket office.
If you love theatre register with MyBoxOffice which gives you excellent discounted offers (sometimes free except for booking fee) on shows, concerts and other events being performed in London.
If you have children under 16 you can take them to see West End shows for free during the month of August as part of a annual Kids Week promotion (It lasts a month despite the name). It is likely you will need to book in advance as the promotion is understandably very popular.
If you have time we suggest you go down to Leicester square to purchase tickets from the box office where tickets are quite often heavily discounted.
London is home to a large pub theatre scene that can be great value for money seeing plays in a intimate setting.