First step is to get a dream diary next to your bed to write down any dreams before you forget them (note: you forget dreams faster when you move your muscles, so try to write down without moving too much). In the long term, this makes you greatly improve recalling of dreams, which include lucid dreams. see also http://www.lucidity.com/NL11.DreamRecall.html
After that, you need to develop a trigger to distinguish between dreaming and awake states. One idea is to look at a clock, then look away and look back to it - if you're in a dream the display will be completely different each time. You need to repeat this regularly when you are awake - by habit you will repeat this in your dreams too.
Once you successfully discover you're dreaming, don't get too excited! Being to hasty to do stuff in your dreams will most likely make you wake up. You need to appreciate it calmly. see also http://www.lucidity.com/NL7.34.RU.SpinFlowRub.html
Also, the dream maker in your mind will attempt a number of tricks to make you cease the lucid dreaming and get back to regular dreaming, such as false awakening https://en.wikipedia.org/wiki/False_awakening - it seems that the mind is really invested in having dreams where you're not aware you're dreaming, that you forget as soon as you start your day.
So I made a tattoo on my hand not to forget to do reality checks. I got used to it and doesn't work :)
So my technique is find some situation I'm in pretty often in both dreams and in real life, and do this check every time in that situation. After a while it's like a reflex and sometimes I even think I'm surely not dreaming and get surprised.
I still couldn't shake the feeling though and I attempted it twice more before giving up and concluding that I was just groggy and needed to hydrate so got up and went to the kitchen to get some water. Of course, I suddenly wake up with a jolt. The entire scenario was in fact a false awakening and my brain decided to cuck me.
I think for the reality check to really work, you need to not just perform it but really mentally try to will whatever affect you think will break the illusion. The problem with the above scenario is that as I was performing the reality check, I was doing it idly so my brain could easily emulate the expected effect.
the physics in my lucid dreams are generally quite grounded so I only managed to fly after my third lucid dream. Dream control != dream lucidity. They are separate skill sets that you need to train independently.
The second necessary component is developing your dream recall (it's no use having lucid dreams if you can't remember them). You do this by writing down your dreams in as much detail as possible every morning when you wake up. At first you may only remember a couple of dreams every month, but do this often enough and you'll eventually work your way up to remembering 5-10 dreams every night.
Watches misbehave in dreams, look at it twice to sus it out. Usually the time changes between peeks.
Light switches. They seem to never work in dreams.
Pushing your hand through your chest. This trigger is very easy and quick. Put your fingers to your chest and push against your ribs without look down at your hand. If dreaming the hand will go through without any effort.
Generally our dreaming brains don't seem to deal well with permanence. The trick is to make it a habit to check if you are dreaming regularly, and at some point you'll do it instinctually in a dream and realize that its not reality.
It happens to me regularly now, probably something on the order of 1-2 times a week. However, I usually wake up rather soon after this realization, especially if I attempt to exercise any control over a dream, which makes it not very exciting, to be honest.
At the time I was also staying at someone else's house so I had that weird feeling of sleeping under a different roof.
Also the whole time I was on the verge of waking up, I could feel my body and had to be careful not to move it while moving in my dream.
I otherwise do not have a natural talent for it, and have done it very rarely.
Here is link to my past comment about it: https://news.ycombinator.com/item?id=25248553
Everyone says they can't do this because they don't remember their dreams, but if you start trying to do it, you will probably find that when you have just woken up, you remember a little, and as you start writing, more comes back to you. Over days of doing this, you will get better at it.
After doing this for a while, try to recognize patterns, particularly specific things that show up with some frequency in your dreams that are indications you are dreaming. For example, there is someone you went to high school with that you encounter semi-often in your dreams, but never see anymore in real life. If you are talking to that person it means you are dreaming.
Try to brainwash yourself, really drill into your head over and over, that when you see this person, you are in a dream, and you should start trying to activate your mind and be conscious of what is going on. Also, really drill into your mind the idea that if you every find yourself vaguely wondering "am I dreaming right now?" the answer is ALWAYS yes.
With luck, the next time you encounter this situation in your dream, there will be a nagging feeling that there was something you were supposed to remember, and then you'll realize what it is and start to wake up your mind within the dream. After a few times, your mind will start to recognize when it is in a dream and become lucid sometimes without the specific trigger.
This is the technique I read in a book decades ago in my early teens and didn't expect it to actually work, but it did. I don't get there regularly (and never did), but I still get to full on lucid maybe once every month or two and it is amazing. It's so incredible to be able to look at the world around you and realize that everything you are seeing is created by your mind.
It gives a deep appreciation for how powerful your mind is and how much more there is to it than just what you are conscious of, since in the dream your conscious mind feels the same as when you are awake, but you know that all of the seemingly external stuff around you and even people that you speak to are also "you". If your conscious mind and everything that seems external to it are really part of the same connected whole when you are dreaming, could the same be true when you're awake?
Even if this approach doesn't work for you, keeping a dream journal for a while can be super interesting anyway.
FWIW, this was the book: https://www.amazon.com/gp/product/0805025006/
I haven't seen it in decades, so can't really vouch for it too much. From what I remember, it explained the approach I've outlined above in not much more detail than I just did and most of the rest was filler talking about what dreams are.
With short sleep, one sleep to deep for that.