I can actually answer this one. Like most questions, the answer depends on the context. Did people hack and slash like madmen? Yes. Did people fight with skill? Also yes. I point first to the manuscript commonly known as Pseudo - peter von Danzig. This contains an anonymous explanation of Johannes Liechtenauer's poem of the use of the long sword. It describes in great detail the skilled use of the weapon, primarily against other masters. It does describe at points the tactics of "those who run in" and "Buffaloes" who are not skilled with the sword. Swords have a principal of leverage to them and while strength absolutely does matter, skill tends to get you farther. In Fiore di Liberi's manuscript (the Getty, If I recall correctly) he similarly describes the "peasant strike" as an over committed downward strike.

But these are weapons made to kill and they are effective at it. The manuscripts both describe "plays" in which an attack will lead to a counter, which in turn leads to a counter and so on. The longest one I can think of is the Zwerchhau play that ends in one death and another wound. It is approximately five distinct moves Long and takes seconds to execute. Most sword fights started and ended quickly. No fighting manuscript from medieval Europe seems to indicate that such affairs would be lengthy, and often emphasize quick bursts of strength to avoid drawn out conflict, Liechtenauer's students say frequently to "come before him quickly and strike to the head or breast so he may not come to blows" or to "drive at him thus with all your strength."

Ms. 3227a in particular spells out a brutal message:

You should execute begin, medium and end in one rush without break and without being stifled by your adversary and under no circumstances let him gain the opportunity to strike.

And

fence upwards from the left side with the whole body and with all strength, to the head or to the body wherever he may hit. And never strike to the sword but just work like would not have a weapon or if you don´t see it, and should not avoid Zeckrühr or taps, and permanently be in motion, work and contact, so the opponent may not come to strikes.

The plays described are complex thereafter. Describing quite verbosely how one is to execute each technique.

Gloss: Mark, this is called the twofold Failer, drive it thus: when you come to him with the pre-fencing, then stand with your left foot before and hold your sword on your right shoulder, and when he is even to you, then spring well against him with your right foot on his left side, and do as if you would hew him with a free Thwart-strike to the left side of his head, but pull the hew before it hits, and spring with your left foot on his right side, and strike there to his head. If he parries and you hit his sword, then spring over to the same side near him, and slice him in his mouth with the short edge, behind his sword with the Doubling. Or fall in with your sword over both arms with the slice.

You can read the manuscripts mentioned here over on Wiktenauer, a collection of treatises for western martial arts. Here is the link to Danzig. http://wiktenauer.com/wiki/Pseudo-Peter_von_Danzig

We can deduce from these descriptions that, like fighting today, it is done with varying levels of skill.

If you are further interested, please join us on /r/HEMAscholar, a collection of papers and articles on the topic or /r/wma, the less stringent community devoted to the revival of these arts for many reasons, not all of which are devoted to their historical context. I would warn scholars reading this that the community is prone to conjecture, and while there are many historians and anthropologists involved, they are outnumbered by less academic enthusiasts.

Although I'm not an expert on medieval fencing, I wrote this answer on medieval military engagements which might help you get a bit of an idea of what combat was like at the time, while this other answer gets into more details directly related to your question.

I actually have a sub question for this

Game of Thrones is infamous for brutal realism when it comes to all sorts of facets of the slightly altered mediaeval life, be it sex, war, death etc. Do they achieve that with their sword fighting? If not then what piece of media has depicted to sword fighting closest to what it might have been in the ancient times?

Where is a good source to read about HEMA techniques?

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