Having leveled several Heroes to 110 now let's talk leveling! As you may know, the level cap has been raised from 100 to 110 and each level takes approximately 2 hours to achieve, bringing the total time spent to hit max cap to 20 hours. Of course the time may differ as somebody may be faster and/or slower than the other but this is the average.
Quests remain the only efficient means of leveling in Legion. It doesn't really matter which zone you enter first, the amount of XP gained, quest reward item level or mob health will be flexibly adjusted to your current level.
1.) Zone leveling:
Simply visit your Order Hall and choose a strike point (one of the four leveling zones on Broken Isles) - Highmountain, Valsharah, Azsuna or Stormheim. Once you unlock Order Hall, make sure to go to the Missions table and pick a Bodyguard. He or she will accompany you on your leveling journeys. I forgot about it twice which was a pity.
2.) Be precise!
Complete quests in a zone from start to finish! Don't just complete a few quests, leave the zone and pick a different one. It may happen that during your leveling from 109 to 110, you will have difficulties finding quests and will have to spend valuable time to find where you left off. This won't happen if you complete every single quest in a zone. You don't have to necessarily complete every single one, just those that count toward the Broken Isle Loremaster achievement. Completing zone quests that yield pillars of creation will yield item level 800 loot which you can attain at early levels! Mind that completing all zone quests will unlock a single dungeon quest which also grants tons of experience. More on dungeon leveling can be found below.
Forget it. Blizzard has totally eliminated leveling through dungeons in Legion. They want players to experience new content via questing and as dungeons have proven to be efficient ways of leveling back in Warlords of Draenor, the experience gained in Legion is so low that it isn't even worth running a dungeon if you don't have a quest to finish there. Note that once you complete all quest in a certain zone, you will receive a single dungeon quest worth approximately 140K XP, which is the only time when it's worth queueing for said dungeon. Otherwise, dungeons just aren't an efficient leveling method. You gain 500 XP per mob kill and on completion you get like 13K XP which is less than a single quest would yield.
Leveling in Numbers
If you want some numbers, I can tell you a single quest gives you anywhere between 15 - 16K per quest (100 - 110). Note the experience gained per quest starts at 15,000 XP / quest and it is slowly adjusted to almost 16,000 once you reach level 109. A single mob kill usually yields 500 - 575 XP, while an easier mob kill is half the XP, so that's approximately 250 - 275 XP. The same goes for dungeon mob kills. Then there's this dungeon quest that awards 140K XP.
Artifact Weapon, Power & Spec Talks
I want to level a Restoration Shaman, but the problem is I'm not able to! I need to first reach Level 110 as either Enhancement or Elemental then I can switch to the other specialization. What will happen to my Artifact? Should I save up all the items that award AP to boost my other specialization (the one I plan to pick at 110)? These questions have irked me as well. Answers are really easy.
1. Healer Leveling
While certain classes can level even in a Healing spec (example Being Discipline priests), it's rather inefficient to level as Healer. Your survivability may be better than usual, but the time it takes to kill a single monster is doubled when compared to a DPS specialization, which is why leveling as a Healer is a bad idea.
2. Artifact Power & Weapon
Choose your primary Artifact at Level 100 (the specialization you're gonna be leveling with). Pick the other specialization Artifact at Level 102 (the one you plan to main at 110). For example I want to main a Restoration Shaman at 110, but first I will have to level him up as Enhancement that's why my first Artifact pick is the Enhancement weapon Doomhammer and the second one the healing mace & shield at 102. During questing, you're rewarded Artifact Power. Try to save it all up for your main specialization Artifact at Level 110. This way, you're not going to be rid of any important Artifact Power later on. While there is a small tolerance claiming you can put up to 13 Traits of AP in your other off-spec Artifact weapon, why making things complicated?
3. Will my non-upgraded Artifact Weapon be powerful enough for efficient questing?
The answer is simple. Yes! I've feared that by not picking traits the weapons would be weak and I'd have problem killing stuff. Guess what? I didn't have any single AP spent on the Enhancement weapons, yet I was still able to kill stuff fast. The only thing I really used to upgrade the weapon item level were Relics from quest rewards. Make sure to use them to upgrade your weapons (they start at item level 750). Throughout leveling you can upgrade them significantly enhancing their power. Save up all the Artifact Power gained for your other weapon (the specialization you plan to main at Level 110). That's the way I did it with my Restoration Druid.
Basically this is the first expansion where Blizzard wants us to level in a formulated manner. You want to skip Order Hall? Have a powerful Artifact? Well, you can't!