With chainmail/ mail and plate armor being introduced to combat, how do medieval soldiers even kill each other? I know they can still kill armored opponent like snapping their necks, using spears, blunt force objects, etc. But the most used weapon in the middle ages is the sword. So how do knights equipped with swords penetrate armor? Not even sharp swords like Katanas can cut through it. My first guess is that they keep bonking people at the head since it still hurts even when using helmets. Im no armor expert, so its up to you guys.
Leaving aside the question of whether a sword was the most used weapon for a moment, you're absolutely right to question how do you even use one. It most certainly was not like a modern movie or videogame, where strong warriors are easily hacking and thrusting straight through mail or plate armour. Wearing armour is pretty hot, heavy and inconvenient -- professional soldiers would only do it while it still provides substantial advantages for their safety.
Fortunately, we can take a good look at parts of this question through the late medieval fechtbuch literature. Fencing books (fechtbuchs) largely appear in the 15th century and are immensely valuable for questions like this, since they provide a technical discussion of how to fight with various weapons. While you can ask legitimate questions about how widely the specific systems in these books were practiced & shared, they give us an excellent glimpse into some methods of fencing which were known to a select few.
One of the most popular fencing traditions in the modern study of HEMA (Historical European Martial Arts) is the 'Liechtenauer' tradition. A large number of Liechtenauer authors discuss combat in (plate) armour with swords, so we can look at what they suggest for ways to overcome this issue:
leder vnd hantschuech
vnder den augen die plössen recht su°ech ~Leather and glove
Correctly search for the openings under the eyes
(Rome Cod 44.a.8 58r, trans. Stephen Cheney)
This is a consistent recommendation: when someone is wearing armour, attack them in the gaps of that armour. The word 'plöss' here literally means 'exposure' or 'nakedness', it has a very clear sense of vulnerability and openness. Armour is not complete -- to actually fight, the person inside it has to be able to see and breathe and move. In order to allow them to do so, there are joints and openings in the armour. A sufficiently pointy weapon can be inserted into any of these openings to injure or kill the person inside. In his book "The Sword in the Age of Chivalry", Ewart Oakeshott relates an account of French and German knights fighting, where the Germans were heavily armoured and taking the victory. Then a Frenchman noticed that while the Germans raised their arms to strike, an opening became available at the armpit, and the cry went up to strike there.
However, it's important to remember that the weak points of armour are still far better than not wearing armour. Yes, a fighter in a full armour will have to remember they can be stabbed in the eye, or the palm of the hand, or the back of the knee. But one out of armour can be stabbed or cut anywhere on the body -- which is a far riskier and more dangerous situation to be in. Ian LaSpina discusses this point at length in his video, "Vulnerabilities Don't Render Armor Useless", which is definitely worth watching.
It's also worth noting that a weakness may not be total. The choice isn't just bare flesh or hard steel plate. Medieval armour was layered and designed to mitigate weaknesses where possible -- one of the most common ways to do so was the addition of mail elements in the gaps between plates, such as in the armpits or elbows. This makes it far harder to exploit that opening. Turning back to the fechtbuchs, they do give a recommendation for this problem as well: first set the point of your sword securely into that mail, then brace the hilt against your body to drive it with your whole weight. This allows the fighter to exert far more force into the weapon, driving it like a lance through thin parts of the opponent's armour. Again, the concentration & focus required to do this is difficult -- the armour is giving a distinct advantage to its wearer -- but it is possible nonetheless to do. Late medieval sword designs like the estoc, which are stiff spikes designed wholly for thrusting, would be perfect for this sort of use.
A third major point is that not all armour is complete. Particularly on the battlefield, the advantages in mobility and situational awareness from wearing partial armour can be substantial. Or another reason can simply be the reduced price. A grim example of this is the Battle of Visby, where an under equipped peasant army was smashed by the Danes -- while the mass graves they were buried in contain plenty of body armour, there is very little leg armour present, and a great many corpses show signs of substantial injury to the legs. When your opponent has unprotected arms or legs, you can simply hit them there and avoid the problem of dealing with their armoured body.
This isn't just a battlefield situation either. Jacques de Lalaing was a famous knight of Burgundy in the middle of the 1400s and gained particular renown for his performance in tournaments and chivalric duels. He was known to frequently fight such duels (with sharp weapons) without substantial parts of his own armour as a show of his own bravery and skill. Writing at the end of the 15th century, Pietro Monte discusses the use of light (partial) armour for travelling and skirmishing, which were far more common in medieval warfare than pitched battles -- when you're not necessarily expecting to be in a fight today or this week, wearing full plate armour the whole time rapidly becomes incredibly tiresome. Another fun source of stories on this line is the autobiography of Götz von Berlichingen, but this hasn't yet been translated into English (at least that I'm aware of).
So to sum up: often your opponent might not be wearing full armour anyway, and then you can hit them in the unarmoured areas. If they are wearing full armour, it will have gaps for movement and breathing which you can attack them through, but this is substantially more challenging. Armour was popular because it worked, but it was still not perfect protection.
Assorted sources:
You might be interested by this answer by /u/MI13 about weaponry in the age of plate armor.
Oof I used the wrong terms with the swords being the most used weapon. But for now it will only be involving swords and how do medieval soldiers kill armored opponents using it.