It's time to do this again! I am bringing this back for nostalgic value along with a way for you guys to support me! Now keep in mind I am sending the very first original version of my leveling guide for Horde (I did not make an Alliance guide back then). This is not really meant to be used to level through WoW, even though you could use it for that purpose. My website JoanasWorld.com contains the latest up-to-date version of my leveling guides which have changed a lot over the years.
The quickest way to level up is to travel through the game's zones, completing all the quests you encounter along the way. Completing quests grants you Experience points, which will slowly fill in your experience bar with blue or purple. When the bar fills, you reach the next level. Alternatively, you could choose to run Dungeons or Battlegrounds, which are not covered in this beginner's guide.
This is something that people really need to start to understand, not just for Classic or WoW but software developement in general. Fixing a bug isn't just flipping a switch or changing a single digit. You have a machine with literally hundreds of thousands of parts, designed by dozens of different people at different times over the course of 20 and more years. You change a single thing and it might break 50 other things in very subtle ways that might not even emerge until months later (i.e. the very high M+ keys some players got at the start of BfA).