These are not the Cards you are Looking for
An article on dueling psychology
A skill with psychology can be applied to many different things. A children's card game, however, is one of the last places you'd think to use that skill. When you compare Yu-Gi-Oh! to typical card games like poker, specifically 5-card draw, you will see that both Yu-Gi-Oh! players and poker players will start their games with a 5 card hand that only they know. Psychology is a way of making guesses as to what those 5 cards are based on what your opponent does, and this comes at both basic and advanced levels.
As an extremely basic example, let's say your opponent makes a mistake on a system like DN. They set a card in face-down defense position, then pick it back up and set a card in their Spell/Trap zone. Almost anyone could now tell you that they just set an Artifact card. Logic like this can also be applied to trickier circumstances, but it obviously takes more knowledge with psychology to do so.
One of the most important advanced techniques for working out what cards your opponent has is to question why they are doing what they are doing. A very common situation is where your opponent will think for some time, then set a card in face=down defense position. This means one of two things; on the one hand, it could be that no card in their hand is ideal for being set face-down, which would imply that the card on the field is not going to cause you any harm if you attack it. On the other hand, it could be that they have more than one potential action to make, and had to choose between the two. This is obviously far worse for you, as along with whatever they just set, they also have some other nasty trick to pull on you for next turn. In these cases, you might be able to tell which is the case through further logic, and this will definitely increase your chances of winning as any risks you take will be minimalised.
An example of something you can almost always ascertain from a given situation is when your opponent has a Spell/Trap card to play in your turn. If you are in an aggressive position with a high-attack monster, and your opponent Normal Summons a monster with lower attack, they have some kind of Spell/Trap to play. If they had a card like Honest, they would probably have attacked in their turn, and so it is very important to remove the backrow that they have if possible. Something else to note is when your opponent is bluffing; if they deliberate and think before setting a card, then the same situation applies as with the setting of a monster: it is probably not ideal for the situation. Setting a card in the Spell/Trap zone, however, carries no further risk than the cards already in the zone, as Heavy Storm is banned for this format. As a result, the only reason a person could have to think before setting a Spell/Trap is that it may be too valuable to lose to a MST instead of a different set card. Real Traps and Quick-Play Spells are set instantly, with little to no exception. Against experienced opponents, you can use this knowledge to your advantage, and set a bluff card immediately after drawing it when in a tight spot. You should also pay attention to what they do with the card they draw. If they set a card that they did not draw last turn, then it is probably not a real Trap. This can be easily worked out; if it was a Trap, then why didn't they set it before? Asking yourself questions like these is very important to knowing what kind of cards your opponent has.
Lastly, keep track of what your opponent has. If they search cards and do not use them immediately, knowing what is in their hand can be vital to determining the rest of their hand. If you are in an offensive position and know your opponent has a Green Gadget, a card they just drew, and another unknown card in their hand, and they set the unknown card in Spells/Traps and the card they just drew in face-down defense position, then you could probably guess that they drew another Gadget. They are evidently unable to make an Xyz play with the card they just drew and ended up setting it in order to protect their life points. At the same time, you would work out that the Spell/Trap they set is a bluff to try and prevent you from attacking the face-down, and because you know this you could work out that they do not want you to attack the face-down card. On that basis, you would have a second reason to believe that destroying the face-down will definitely not be advantageous to your opponent. The true situation will often have more than one logical route to it, and by working out this true situation you can generate some kind of advantage.
So, if you're wondering how this knowledge can translate to power, it's actually quite simple. If you know that your opponent's Spell/Trap is a bluff, you can ignore it and carry on attacking. If you know that your opponent does not have a card like Fire Hand or Ice Hand set, you can make an aggressive play rather than summoning something like Abyss Dweller because you're scared of the possibilities. Psychology does NOT let you mind crush your opponent. However, it DOES let you use the card "Mind Crush", as long as you can work out the kind of cards in their hand. That is essentially how this works; it's not a magical power. You just need a strong sense of logic and a good memory to work out what your opponent's cards are.
And that's the psychology behind a children's card game, which actually cuts pretty close to the psychology in poker. 5 cards each, work out what's in your opponent's hand and learn to tell when they are bluffing. The skills needed and the goals are exactly the same, but there's one major difference. In Yu-Gi-Oh!, 90% of your opponents will not be applying psychology to the game to work out what's in your hand. If you can pull this kind of thing off, you'll have a major advantage, and will be able to rely far less on luck and chance.