Short (like real short) introduction. Lucid dream is the state when you realize that you are dreaming. Fantastic feeling, I don't think I've even experienced anything as euphoric.
I feel lazy to describe the basic principles, you can find them at www.spiritweb.org.
Sometimes, when I am asleep, I get a feeling of unreality and desire to check, whether I am dreaming or not. Before, in cases like this I would share my doubts with somebody else in my dream - and everytime time they proved, just as 2x2=4, that everything is in order and I am not asleep.
Another well-known method doesn't work either - in my dream I can pinch myself and feel the pain without further delay. All the signals of perception organs are emulated when I am sleeping.