Important note: This is still a work in progress. Some information may be missing.
You may or may not have heard of lucid dreaming. If no, prepare to be surprised. What is detailed here does sound a bit unreal, but it is scientifically proven. If yes, this site aims to give the most certain parts (since lucid dreaming is associated with a lot of esoteric nonsense) and to show the basics.
What is this thing you call lucid dreaming, anyway?
A lucid dream (LD from now on) happens when you are inside a dream and you are aware that it's a dream. Typically, you have no control over your dreams and only you wake up do you realize that it was a dream. When you get this control, you can do pretty much anything you want. If you've been in virtual reality, imagine this as similar but far, far better. You can do things not possible in real life, like flying. You can shape the dream, so you can visit any place you'd like to (provided you have any idea what it's like) or a place not existing in real life (like Hoghwarts).
Apart from this, it's important to realise what LDs are NOT.
1) LDs aren't just a crazy theory. There have been experiments conducted to prove their existence. Basically, the person in the dream moved their eyes in a preset pattern to communicate.
2) LDs aren't esoteric. All the processes happen in your brain. They don't help you connect to the astral plane, have shared dreams, get telekinesis etc. because that stuff isn't real.
3) LDs aren't profitable. You may find people trying to sell you courses on the topic, herbs for better dreams, or other things without any guarantee they will work. All the info is online, as you can see right here, so it's pointless to buy courses. No herbs necessary, either.
Step by step guide
Step 1: Sleep well
Duh. Our first goal is to get regular dreams. In order to get an LD, you should first have a vivid dream. You know, the type when, after you wake up, you are confused for a few moments and only then realise it was a dream. To get any dreams, let alone vivid or lucid ones, you need to sleep enough. "Enough" isn't very precise. Here's a way to find out how long you should sleep: On a weekend, go to sleep once you get tired. Preferrably don't do anything that could disrupt your sleep cycle (like drink tons of coffee in the evening). Check how long you slept. Substract an hour (you tend to sleep more in the weekend after not sleeping enough during the week). This should be your sleep length. Of course, preferrably you should sleep long enough not to need an alarm clock, bt that isn't very reliable and can cause problems if you have to wake up earlier than you would normally.
Don't drink coffee or preferrably anything with caffeine for a few hours before sleep. Try to keep a stable sleep cycle, going to bed at the same time every day.
All this advice is relevant just for good sleep and isn't specifically dream-oriented, so you can follow it even if you have no intention to lucid dream!
Step 2: Keep a dream journal
At this point you should remember a dream every day. But only for a few minutes. Dreams fade very quickly, probably because of their nonsencial nature. You have to keep a dream journal (DJ from now on). Without it, you won't get anywhere. It's really simple: When you wake up, you write down your dream. Or maybe you wish to instead record you retelling the dream (and possibly transcribe it later). There are many options. So how do you choose?
For starters, ignore anything that requires more than 15 minutes every day. It will probably get tiring over time and you'll stop. The goal is to remember as much as possible with as little time spent as possible. At first, just give each dream a serial number, a name if possible, and a description. Use footnotes to add parts you remember later.
Don't complicate this. Some people would suggest recording and transcribing, or dream signs, or other complications, but the main goal is just to have the dream written down quickly. After all, you don't want to lose an hour of sleep.
Of course, now is the time to actually get lucid!
Step 3: Reality checks
There are two ways to get LDs. Habits and techniques. Habits are performed during your everyday life and consist mostly of reality checks. Techniques involve messing with the way you sleep and doing specific things before sleep. They take more time and are more advanced. Most importantly, you still won't get anywhere with them if you don't practice reality checks (RC from now on). So what are these, anyway?
There are some actions that yield different results in real life and in dreams. Well, technically, almost all of them do (like jumping out of a window), but a few are predictable and safe (which jumping out of a window isn't). The goal is to frequently do these things in everyday life, and you'll some day do them in a dream, too. A few such actions (Reality Checks or RCs) are these:
1) Pinch your nose and breathe in. In real life, you won't be able to, in a dream, you will. Simple as that.
2) Try to push a finger (preferrably your finger, it's pretty hard to explain otherwise) through your palm. In real life it obviously won't work, but in a dream, you will be able to (after a few tries).
3) Look at your surroundings and think about whether they make sense. Recall how you got where you are and question your actions (do they make sense?). It's not very reliable, but it's useful to avoid the "obviously real" trap (in a dream, you're so confident in reality that you shrug off RCs as unnecessary).
So the ideal situation is like this: You perform these a lot in real life, and eventually, you'll do it in a dream and get an LD. This would be great, but there are two catches:
1) Just doing an RC whenever you remember isn't very good. For this to work, you would have to remember 10 times per day or more. It also means that you get little control over when you'll do an RC in adream. You have to rely on luck.
Solution: Learn to do RCs whenever you move somewhere. It is very rare to be sitting all the time in a dream; you always walk or run or fly. So any time you begin walking, do a quick RC and reflect on the results. This is important, because when you're in a dream, you might just think you're not holding your nose enough or make up some other excuse. Reflecting on the results means a little bit of thought.
2) Okay, so we know when, but what to do? If you find out you're in a dream, you'll probably run around with no idea what to do. Or lose lucidity. Or wake up in five seconds. (All of these have happened to me).
Solution: Have a plan. RCs aren't the only thing. You should know what you want to do in the dream (more on that in step 4). Whenever you do an RC, repeat mentally your plan and look around. Focus on random objects around you and study your surroundings. This will serve as an RC in itself, since studying your surroundings will yield something obviously wrong in most dreams. But more importantly, it gets you focused. Even if you wake up immediately, you'll be able to remember that moment better and you'll be able to tell more about what the dream was like. If you skip this step and get an LD, the world will feel fuzzy and unclear. You will have problems figuring out what to do. By shifting into focus, you can get the five seconds of rational though necessary to get an idea what you're doing.
Step 4: Enjoy the dream
Once you're in the dream and it's clear, do whatever you want! This is the selling point of the whole deal with LDs. Once you are in a dream, you get roughly 10 minutes of time to do whatever you want. Before we elaborate on this, the issue with time. It's... confusing. Ten minutes is a lot. Imagine writing down ten minutes of your life. Add to this that you forget dreams way faster, so you have to write more details. This means that 10 minutes is a bit optimistic. You get roughly 5 to 15 minutes, but as with any dream, you inevitably forget most of it. You could realistically write down 5 minutes. The whole issue with time is even more complicated, since there's dream (subjective) time and real time, and there's not enough research on this. The positive side of this is... ten minutes is a lot. And time is subjective, so it may feel like more. Even though you may forget most of the details, if you have a strong feeling (like from flying the first time), you will remember it.
Without further ado, a few ideas:
1) Just walk and look around. It's an awesome feeling to touch things, see things, hear things and know that it's all just your mind. The dream tends to be very surprising, just like any normal dream. This depends on what your normal dreams are like. If you often have nightmares, just remember that you can wake up just by shutting your eyes and shouting "WAKE UP!". If you have them very rarely or not at all, this might turn out to be good enough for a few LDs.
2) Talk to people. Try debating about your life, or anything, really. Sometimes it's just bizarre (and cool), but sometimes you might get some interesting responses. Ask people if they know it's a dream.
3) Fly around. Yup. You can do that. It's a dream, and doesn't have to make sense. Generally you can do anything you can reasonably imagine. Make things levitate (Technically speaking you have full telekinesis in dreams. It doesn't get you any special powers in real life, though. Obviously.). Summon a dragon. Or a time machine. It won't get you to a time period you don't know of (Nothing gets you info you don't already have. You're in your bed all the time and most of your senses shut off, so there's no way for it to get into your brain.), but you could visit the dinosaurs. But flying is one of the best. You can just levitate or use any gadgets you feel you need. Hover around. Concentrate on how the thing feels and know that it's possible. You'll make it.
In the end, you'll more probably have a surplus of things to do than run out of them. There are many lists of names like "101 things to do in a lucid dream", so you can always check these if you need.
Step 5: Techniques and advanced stuff
The first four steps should be enough. But there are additional things that may help you. It's not that important to list them here (any site about lucid dreaming has some techniques mentioned), but what is important is how to deal with them. An easy way to grind your progress to a halt is to try a new technique you found every day or so. Many of them require you to somehow alter your sleep habits, which should only be done if you're sure it will lead somewhere. Only try out "advanced" ideas when you either are already getting LDs regularly or when you are really desperate. Get some idea of what you're supposed to do, and try to find the same technique at several places. Find some results, whether good or bad. There are a few common ones, usually of names like MILD or WILD or similar. Try these out first.
So, that's it? Maybe. Another cool thing the brain does.