It's a place where you will learn..
To face your fears, retrace the years
And ride the whims of your mind...
Commanding in another world
Suddenly, you hear and see
This magic new dimension...."
From Silent Lucidity, by Queensryche
Lucid dreams are those dreams where you look around yourself, while still in the dream world, and say "Hey, this doesn't look quite right.. Dogs don't have 6 legs! This must be a dream!" At that point, most people either wake themselves up from the excitement, forget their realization and continue on, or start to control the dream. And you can control the dream, while in this state. Want to fly? Go ahead. Want to be a bird? Sure.
Lucid dreaming can be accomplished fairly easily, too. If you're determined and willing to take time out of your life to accomplish this goal, that is. You have to start at the beginning though. You have to remember your dreams. "But I don't have dreams", you say. Everyone dreams, most dream many times a night. It's necessary for your survival.
"How do I go about remembering my dreams, then?" Well, the REM period of your sleep cycle (When you dream) starts about 3 hours after you lay down (Varying depending upon how tired you are, your activity during the day, and how much sleep you've been getting), giving your body sufficient time to relax and repair itself. You can speed up this time by doing relaxation exercises before bed, and getting more sleep. Either way, you should set an alarm to go off after about 5 hours of sleep. Make the alarm nearby, so you can shut it off quickly and it doesn't drive the dreams out of your mind. Likewise, make the alarm as non-obtrusive as possible. Quiet music works well, in most cases. Soft music, too, not Rage Against the Machine, or your dream will be gone from your mind as quickly as if you'd been waken up by a pair of cymbols clashing right next to your ear. Waking too suddenly invokes an immediate return to conscious thought, as your brain thinks you've just sensed danger. Dreams take a lot lower priority than danger, so out they go. Poof.
You should have a dream journal and something to write with next to your bed, on the floor or nightstand. This can be a notebook, a tape recorder, anything you feel you can use to record your dreams. If using a notebook, a small, unobtrusive light source should also be available. I use the glow from my computer screen, across the room. Use whatever you want to, a nightlight works well.. If you can't remember the date after just waking up, ignore it but remember to come back and date your entry when you're more awake that day. This is important to chart your progress, or to look at what else has been going on in your life at the time that might have inspired the dream (If you want to do dream analysis.)
Once you've been able to remember your dreams, it's time to start working on lucid dreaming. There are several methods of accomplishing this. One that works fairly well is to get into the habit of asking yourself 10-15 times randomly during the day "Am I dreaming?" And then try to change the floor color, or read some text, look away, and read it again. (Text usually doesn't appear the same way twice in dreams.) Do this daily for a few weeks, and soon it'll become ingrained into your mental programming, and you'll probably start asking yourself while dreaming, too. One way to do this is to keep a small piece of paper on your person with the words "Am I dreaming?" on it, and look at it, making sure to test your reality as well, randomly throughout the day.
Another method is to do a relaxation exercise as you lay in bed, affirming to yourself before you go to bed that you *WILL* realize that you are dreaming tonight. Then, you relax everything... including your mind. You let your mind wander, but try to keep a relaxed awareness, not letting yourself become distracted by the hypnagogic imagery (The weird stuff you see before you actually dream). If you've meditated before, it really helps with this. When your awareness progresses into REM sleep and dreams, hopefully your conscious awareness will remain intact.
But what about waking up early? You let the excitement of realizing you're lucidly dreaming overtake you, your body feels the adrenaline and decides it's Wakeup time. One solution to this problem is spinning. Spin yourself around and around, and when you stop, you should still be in the dream. Spinning helps to "center" you in the surreality of the dream world. There are other options too, like staring at your hand. Anything to further immerse yourself in the illusion.