There are a lot of ways to level in classic wow. But mainly there are 3 main paths, some more efficient, some less. These are in order of frequency people tend to use them :
which is just completing quests in your area then moving on. While this may work in retail wow, in classic you're going to soon learn that there simply aren't enough quests to keep you going from 1 to 60 without supplementing your xp gains with other methods, however this is still a good way to get xp and shouldn't be looked over.
these are probably the best way to level from numbers perspective, grinding dungeons also provides you with decent loot for your level and is generally more fun than grinding mobs in open world, with instancing also protecting you from randoms tagging your mobs or random ganks. However this sours pretty quickly if you don't have a dedicated group to play with, since doing runs with randoms generally isn't going to be as fast and you may even wipe, leading to increased repair costs and general bad feels. Also don't forget to look up all the quests you can do in the dungeon you're currently running and ask your teammates to share them if they have them, as they can be good sources of gear and even gold, making sure you get an upgrade for your gear, even if one doesn't drop in the dungeon itself.
this one is pretty much just farming mobs for xp in open world, which leaves you open to ganks and you're occasionally have to fight with members of your own faction over spots, however this method relies solely on you and though its still easier in groups, you can do it on your own. There's also no division of xp, which plagues groups as in 5 man group you will generally get a bit more than a fourth of experience you'd get if you were alone. Now that makes sense in dungeons, however if you're playing a class with little downtime you might find it more efficient to simply grind out the mobs and supplement it with occasional quests. When grinding mobs also be aware of your class's downtime, for example warrior is probably going to have to eat food after a few fights, but a mage that's got decent spirit and is using a wand to finish off fights is probably going to be able to keep going for as long as they want.
These are my thought on leveling your characters in classic. If you'd like to play classic without all the streamer drama and the general unfriendliness ever present in official servers i'd advise you to go to this list of wow servers and find a server that's perfect for you.