How do you Meditate properly?

If you stop breathing then you are doing it wrong.

That's true for almost every activity, except freediving, isn't it?

Yeah, a big can of big worms.

This analogy is surprisingly and unexpectedly? appropriate. Good one, Phoenix.

All this talk about not thinking, empty mind is only for the experts. You are not there yet.

Try this. I am being serious here. Close your eyes and 'see' a can. Then open this can and imagine all these worms wriggling uncontrollably out of it. You are in a state of anxiety, panic even. What do you do? Use you mind to slowly and calmly get them one-by-one back into the can and close the lid.

What do you feel now? Calmer, relaxed, mentally and emotionally more focused?

Repeat this exercise a few times for a few days.

Come back in a week and we can go on to the second lesson. Perhaps by then you will know what the second lesson is without my help.

Oh yes, I can see how the activity of dying could involve the stop breathing part without being labelled as wrongfully done.
In fact, one could almost go so far as to say that it isn't done 100% correctly, if it doesn't involve at least some degree of stop-breathing.
Therefore I stand corrected wouldn't surprise me if you were to come up with another breathless activity tomorrow, to really turn the knife in my wound... sob!

How to introspect yourself (without using sharp objects )?

This is the type of meditation that i use. I Tend to calm my breathing down and mantain as less as possible amounts of thoughts in my mind. If there is something that I want to think about i tend to think about it e.g. Problems i tend to mediate about and attempt to solve mentally.

That would not be correct meditation, according to the Ch'an/Zen school. In meditating, the goal is to end mentation by not clinging to thoughts that arise. If there is something you want to think about, you should recognize that there is a thought there, but then forget it. The solving of all problems comes ultimately not from using the rational mind to think about them, but through the recognition that there are really no problems.
Meditation should develop the ability to use the intuition, which is connected with the "universal mind". This occurs by simply being. Not trying to do anything, not trying to not do anything. It is listening and seeing and feeling, but not making any judgements about what is heard and seen and felt. The intuition leads one to the understanding that there is no self and no others, there is no seperation between any things at all. That is where the answers to all questions are.

Physically, a good way to start meditating is to simply focus on breathing. sit in a comfortable position. (or not so comfortable, like lotus posture, if you want to challenge yourself.) Breath in through the nose and out through the mouth, and take slow deep breaths, not shallow. Try not to close the eyes all the way, as that can bring on sleepiness, keep slightly open if not all the way open. Focus on a single point a few feet in front of you. Posture should be upright, back straight. arms relaxed, resting the hands on your lap. Place the left hand inside the right hand, and touch the thumbs together lightly.
Focus on the breath going in and out, through your body. Thoughts will come up, but just let them go past. If you find yourself thinking something to yourself, following a thought path, just come back. Whatever thoughts come up, let them go, just always bring yourself back to the breath. When you hear sounds, thoughts will arise. They just pass by, and are gone. Don't linger on anything, always come back to the center, to the breath.

There are many ways to meditate, but this is a simple way that is used in Zen. The essential thing to remember is not to cling to anything, just to Be. Always departing, always returning.