How can I prevent myself from doing long, fancy attacks?

For example, if 2 enemies are approaching me side by side, there doesn't seem to be a way to attack one of them without leaving myself utterly open to counterattack or interruption from the other one. I always do an unnecessary windup and lunging or leaping slash of some sort that accomplishes nothing but getting me killed.

This with the "quick attack" left-click button. How can I just swing my sword like a normal person?

If you're standing next to the enemy you're targeting (and you can use Alt to lock a target if you have problems with unintended target changing) and you click the quick attack once, that's as quick and simple as it gets. Being farther away will sometimes cause "fancy" rolls or lunges to close the distance, and clicking many times will lead to combo type repeated attacks.

In general attacking does open you up to counter-attack; obviously the quick attack less than the slow/strong attack. Yes, this means it's bad to be double or triple teamed, unlike in say Assassin's Creed style combat where the enemies politely attack you one at a time. The bigger problems are that getting hit will cause you to stagger, not responding to new commands for a bit, and getting hit from behind does extra damage.

Mitigating these things is key to succeeding in this game's combat. You want to disable groups of enemies as best you can, via signs or traps or bombs. Using your Quen sign (the shield one) not only protects you from damage, but also from the stagger/interrupt that happens when you get hit, so it's quite useful. I find it's also helpful to quickly finish off the weaker enemies first, as lowering the number of attackers is better than eliminating one tough enemy.

Parry is nice for counter-attacking, but it uses/requires Vigor, so if you want to avoid "running around like an idiot regaining vigor" as Matthew says, better to dodge (double-tap a direction to roll that way) than parry while your Vigor is low.

Lastly I highly recommend taking advantage of the potions, traps, and oils as best you can. Don't neglect them like consumables from other RPGs. They're very important to both the character and the gameplay, and using them well will get you past a lot of the difficulty or frustration.