Lucid dream induction is the art of making yourself dream lucidly. In other words, it's how to consciously start dreaming or how to "break into" a dream you realize you're having and take control.
One of the common techniques for inducing lucid dreams is called MILD, which stands for mnemonic induction of lucid dreams.
Don't worry, it's easier done than said!
In essence, this is like putting an alarm note in your cell phone. You're setting yourself a mental note to do something in the future.
Specifically, whilst you are in a dream state in the future.
Decide that you are going to briefly wake up the next time you notice you're dreaming. As soon as you wake, recall as much of the dream as possible. If you're regularly using a journal already, this should be a reasonably simple thing to do.
Then allow yourself to drift back off into sleep. Dr LaBerge, who invented this technique, claimed this is the best time to set your intention for your dream.
As you start to drift, tell yourself something along the lines of "Next time I'm dreaming, I will actually remember that I am dreaming". The exact wording you use is a lot less important than just remembering to tell yourself this, over and over again as you drift back into a sleeping state.
As you repeat that phrase or mantra, see yourself back in the dream you've just been having. Or, if nothing is particularly clear about that dream, another one that you've had recently. If that doesn't work, visualize yourself as though you're watching a movie of yourself dreaming.
Don't concentrate too hard, otherwise you'll stop yourself from going into a dream state and will find yourself wide awake through too much concentrating. It's far better to fall asleep during this process than keep yourself awake with it.
Ideally, do the next step whilst you're still in the process of falling asleep.
See yourself in the dream and notice something that clearly indicates it is a dream. Anything will do for this: a dragon wagging its tail whilst cooking a unicorn with its breath would be exceptionally clear. But its your dream, not mine, so notice anything that gives you a clear signal that you are in a dream state.
Say confidently to yourself "I'm dreaming". But continue with this twilight zone experience and allow yourself to drift further into the land of slumber.
You can use this process to set the intention of your dream at the same time if you want to. It's not essential to do this, but it can help point your dreams in the direction you want them to follow.
Keep repeating the process of setting your intention of remembering to notice when you are dreaming and to tell yourself that you've actually recognized it's a dream when you do notice. With a little practice, you'll start to become accomplished at spotting when it's a dream, not reality. You should then be able to enter a lucid dreaming state almost at will.