You find stuff on your journey, people find stuff on their journey.
You share when they group to do a dungeon and they share…
Boom, you have all the quests (yes I’m generalising and don’t take this out of context).
Just play the game and enjoy your journey.
In the old days we used to wander around games talking to npcs to see if they had anything important to tell us, or a quest or instruction. That’s how many games worked back then. They didn’t all have markers for quest givers, or yellow dots on a map to tell us where to go. 
I think back in the day us old timers would probably want to visit the war chief, he’s an important figure, we wouldn’t need a questie to tell us to. 
Hence it wasn’t thought to be that complicated for new players back in 2004 like it is now. We would also ask each other, hence the ‘where’s Mankrik’s wife’.
Well, it doesn’t really matter that much. You don’t have to complete all the quests to do a dungeon and have fun. There are plenty of quests and you will miss out on a lot of them on your way to 60 even if you know what you are doing.
There is no achievement systems so you can just do what you like and not worry about doing everything.
Works great for me so far. Played with it from lvl 10 to 16 so far.
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You don’t need to install and addon, I personally find this one of the best guides including all the dungeon quests
https://barrens.chat/viewtopic.php?p=16301
You can also use
Only because i dont read epic story about 10 wolf paws , 5 zebra hoofs 3467x time im bfa scrub ok. I hope you are playing on crt monitor 800x600 for true vanilla experience.
A MMORPG it’s an adventure, you have to explore by yourself.
It’s a journey…
(That the authentic experience, you don’t have to know everything.)
Yeah for new players maybe.
I never played classic but wotlk and higher…but these zebra hoofs? Well i remember that 
Im enjoying that all is slower and harder …really but im glad that i dont have to google every third quest. Im not great english speaker as you can see so when i have finally time to play at 1am i dont want to spend my energy into reading story about rabbit ears or whatever. I know story for next 7 expansions.
Indeed part of the appeal of Vanilla WoW is exploration. Quests sometimes take you to strange places, or the one that gives you that important item for completing a dungeon is discovered when you travel to a certain location or do a previous quest somewhere else.
You could do all those quests on your first character, follow guides that allow you to level up the fastest way possible and so on, but that’s optimization: if you’re meant to play optimally by simply playing the game normally there’s no freedom, no exploration, no adventure. You’re meant to see the world and interact with other players, and yes, share quests too.
The alternative is now implemented in retail, where you pick the quests at the beginning of the dungeon and deliver them at the end. But then there’s no “quest”. They could just give you experience or gear the first time you do them - they already do the first time of the day in the dungeon finder anyway.
So to answer op’s post: you don’t have to do all quests. You may miss some interesting items on the way, and some extra experience, but learning is part of the process of the game. It improves replayability because you’ll want to do things in a different way next time.
Funniest is when the quest tells you exactly where to go in minute detail, you don’t follow it, then complain the quest isn’t there. 
My Hubbie today, ‘it says the quest is north east, this isn’t north east and I can’t find the quest giver. This is c…’
I was really confused why he thought the quest giver should be where he is (south east) when he wasn’t where it said the quest giver is. And knew he wasn’t. 
(Raene’s Cleansing quest in ashenvale)
No the problem is that most people have problem with West/East like Left and Right.
Once I was suddently invited in a group in Trisfall Glades bashing some mobs in a field and one of the mate was complaining :
D*** where are those robbers?
Ah, Do you mean the graverobbers? Maybe you should find a graveyard first because we are in a field right now.
… Oh man you are a smart a** / logic…
Once we found the graveyard, there were a tons of robbers.
I installed questie for another run this time with human paladin, and i leveled up faster, still i don’t remember the quests although i played also human warrior 2 weeks before.
Yes I think you are 
Google.
And no this isn’t unique to Classic WoW. Personally every time I started a new mmo I have had to google things, even for modern games. I still do for the games I play regularly because it’s basically impossible to know everything.
It is not, dude. When i was playing the game first time i was new not only into wow, but in mmoprg in general and had absolutely no idea what is going on and how it is supposed to be played. By not understanding the concepts you will miss many things and you can’t help it. Especially those dungeon quests and stuff. However that is not critical at all. And, being a mmo, game encourage you to join some kind of a guild and run dungeons with them so you not have to deal with impatient pugs. Also try to use internet. Wowhead is beautiful base of information and usually you can figure everything out reading comment section.
merra for mvp
This will never happen but thank you for your support 
I mostly ask people where did they get their quests from. My plan is to go every dungeon at least twice. I learn the questgivers at first run, complete them at second run or other runs. Even if getting the quest is too complicated, at least one person in two dungeon runs most likely have it and explains how to get it.
Exploring and figuring these things out is part of an RPG.
You are in fact NOT supposed to know. You are supposed to FIND OUT.
The game is a journey. Enjoy it.