Dream Exit Induced Lucid Dream (DEILD), is where you wake up from a dream (either lucid or not) and then ly perfectly still, and have the intention of going back into that dream, but lucid.
Before you try having a Dream Exit Induced Lucid Dream, first spend about five nights working on being able to wake up from a dream, being perfectly still. A mantra will help. Get the idea in your head that you will remember, instead of forgetting as soon as you wake up. Try thinking something like "I will remain still when I awake." Also work on keeping your eyes closed while remaining motionless. Study the blackness of your eyelids, and say to yourself "When I see this, I will stay still, with my eyes closed."
This'll make your efforts way more easier. Once you got this down, the hardest part of this is done! Now you've now mastered how to stay still when you wake up.
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Now, after you wake up during a dream and you find yourself just lying there, eyes closed, and motionless, now you'll want to think about the dream you just had, or you can even think of a new dream you want to have, though this is harder because the brain then has to "create" everything. Plus this will most likely wake you up. It's best to not do this until you got this mastered. You can also visualize a past dream if you can't remember your last dream.
Now, think of your dream. Stay focused on every aspect of it. What can you hear, see, smell, taste, feel? Let the dream take over you, just don't try to hard, but just let it happen.
TIP: Some times, or often, you will think you are not going to fall asleep, or you haven't fallen asleep yet, when it's actually just your mind messing with you.
If everything goes well, you should soon find yourself INSIDE the visualization, as a dream, not just imagining it. The second hardest part of this is noticing when you are actually dreaming, keeping yourself from not realising it, and then falling into a non lucid dream. Once you're inside your visualization-to-dream state, stabilize the dream, and have fun in your Dream Exit Induced Lucid Dream!