Leveling
Leveling will be divided into 2 sections. Story VS Speed
Story
If you want to experience the full story of the game then settle in for a long and enjoyable ride. Experiencing every storyline from every expansion will take multiple toons. There are several steps involved in accessing every story. First you need to have a character at level 60. My recommendation here is to just play the story as given to you up to the current expansion. Follow the main quest markers to do so. Taking side quests during any of the following is unnecessary to the plot but can provide extra experience or gear and have some have added background stories. Once have a toon at level 60 you need to completed the intro quest A nation divided for Alliance or Speaker of the Horde for Horde. These quests are part of the main storyline for The Battle for Azeroth expansion and will remain as part of the core storyline. Now you are ready to "Story Hop". Return to your embassy in either Stormwind or Orgrimmar and locate Chromie. This can be done on any character level 10 or higher, and it is my recommendation to do this with new characters as "Chromie time will kick you out and back to the latest expansion on reaching level 70. She will have a large hourglass over her head. Speak with her to initiate "Chromie Time" which allows you to choose an expansion to play the main story and most of the side quests. Due to the speed that you level with I recommend consentrating on main story quests. To ensure you don't get kicked out before you have compeleted the storyline for your selected expansion.
Speed Leveling
Speed leveling is going to be a much shorter explanation. First either stay on the core storyline or pick a Chromie Time expansion explained in the Story Leveling section. And quest as fast as you can. There are a few things you will need to do to make this as fast as possible. First build your talents around survivability and AOE. You are going to want to be able to gather as many enemies as possible and nuke them all down quickly. This is done by keeping your gear at max level, having heirloom weapons and armor(you gain these by playing the game a lot), and specializing correctly. Finally make sure you are always queued for a dungeons and/or raid of appropriate level. The random dungeon finder is best of this. Some side notes for this process:Tanks work the best overall. They have fast queue times and are able to gather huge groups to AOE down.(AOE stands for Area of Effect and are simply attacks that hit multiple enemies). Healers have fast queue time but for the most part are terrible at questing. Try to level with a group or using the Dungeon finder while doing only essential quests. DPS will spend the most time questing and should always, always be in queue for a dungeon to help keep gear levels high.